Nicolae Popescu

Nicolae Popescu, Ph.D., D.Phil.
Born	22 September 1937(1937-09-22) Strehaia, Romania
Died	29 July 2010(2010-07-29) (aged 72) Bucharest
Nationality	Romania
Fields	Mathematics,
Institutions	Institute of Mathematics of the Romanian Academy, University of Bucharest
Alma mater	University of Bucharest
Doctoral advisor	Miron Nicolescu
Doctoral students	36, Alexandru Zaharescu, Constantin Vraciu, Mircea M. Marinescu
Known for	Abelian category theory, non-Artinian rings/semi-Artenian rings and modules, Gabriel-Popescu Theorem

Nicolae Popescu (Romanian pronunciation: [nikoˈla.e poˈpesku]; 22 September 1937 – 29 July 2010^[1]) was a Romanian mathematician and Emeritus Professor. Popescu was elected a Member of the Romanian Academy in 1992. He is best known for his contributions to Algebra and the theory of Abelian categories. Since 1964 and until 2007 he collaborated on the characterization of abelian categories with the well-known French mathematician Pierre Gabriel. His areas of expertise were: Category theory, Abelian categories with Applications to Rings and Modules, adjoint functors, limits/colimits,^[2], Theory of Sheaves, Theory of Rings, Fields and Polynomials, and Valuation Theory; he also has interests and published in the following areas: Algebraic Topology, Algebraic Geometry, Commutative Algebra, K-Theory, Class-Field theory, and Algebraic Function Theory. He published between 1962 and 2008 more than 102 papers in peer-reviewed, mathematics journals, several monographs on the theory of sheaves, and also six books on abelian category theory and abstract algebra. In a Grothendieck-like, energetic style, he initiated and provided scientific leadership to several seminars on category theory,^[3] sheaves and abstract algebra which resulted in a continuous stream of high-quality mathematical publications in international, peer-reviewed mathematics journals by several members participating in his Seminar series. His book Abelian Categories with Applications to Rings and Modules^[4] continues to provide valuable information to mathematicians around the world. His latest contributions have also branched into valuation and number theory. He has published over 100 original, peer-reviewed articles in mathematics, mostly in category theory, algebraic geometry, and Galois and number theory.

Biography

Popescu was married, and there is a surviving wife Liliana and three children. He earned his M.S. degree in mathematics in 1964, and his Ph.D. degree in mathematics in 1967, both at the University of Bucharest. He was awarded a D. Phil. degree (Doctor Docent) in 1972 by the University of Bucharest.

In 2009 he carried out mathematics studies at the Institute of Mathematics of the Romanian Academy in the Algebra research group and also had international collaborations on three continents. One found from conversations with former Academician Nicolae Popescu that he shared many moral, ethical and religious values with another famous mathematician French-German-Jewish Alexander Grothendieck who visited the School of Mathematics in Bucharest in 1968. Like Grothendieck he had a long-standing interest in category theory, number theory, practicing Yoga, and supporting promising young mathematicians in his fields of interest. He also supported the early developments of category theory applications in relational biology and mathematical biophysics/mathematical biology.

Academic positions

Popescu was appointed as a Lecturer at the University of Bucharest in 1968 where he taught graduate students until 1972. Since 1964, he also held a Research Professorship at the Institute of Mathematics of the Romanian Academy, which institute was ruthlessly eliminated by former dictator and president of S.R. Romania, Nicolae Ceaușescu, in 1976 for reasons related to his daughter Zoe Ceaușescu who was 'hired' by the Mathematics Institute in Bucharest two years before.

Books published

• 1. Elemente de teoria algebrică a numerelor, Univ. București, 1968. (Elements of the Algebraic Theory of Numbers)

• 2. Teoria categoriilor și a fasciculelor, Ed. Stiintifica, 1971. (Category Theory and Sheaves)

• 3. Categorii Abeliene, Ed. Academiei, 1971. (Abelian Categories)

• 4 Nicolae Popescu. Abelian categories with Applications to Rings and Modules, Academic Press, L. M. S. Monograph No.3, London, 1973, ISBN=0125615507.

• 5. Popescu, Nicolae and Popescu, Liliana. Theory of categories. Martinus Nijhoff Publishers, The Hague; Sijthoff & Noordhoff International Publishers, Alphen aan den Rijn, 1979. x+337 pp. ISBN 90-286-0168-6.

• 6. Selected topics in Valuation Theory (to appear).

Original articles and references

1. Asupra omologiei si omotopiei C.W. - complexelor, Stud. Cerc. Mat., 1962 (On the singular homology of CW-complexes (with D. Burghelea)

2. Diferențiale generalizate, Comunicările Acad. R.S.R., Tom 13, Nr. 6 (1963), 523-528. (with C. Bănică) (Generalized Differential Functions).

3. Quelques considérations sur l'exactitude des foncteurs, Bull. Math. Soc. Sci. Math. Phis. de la R. P. R. 7 (1963), 144-147. (with C. Bănică)

4. Modules à différentielle généralisée, Rev. Roumaine Math. Pures Appl. Tome IX, Nr. 6 (1964). 549-559.

5. Module cu diferentiala generalizata, Stud. Cerc. Mat. Tom 16, Nr. 6. (1964), 791-800.

6. La structure des modules injectifs sur an anneau á idéal principal, Bull. Math. de la Soc. Sci. Math. Phys. de la RPR Tome 8 (56), Nr. 1-2 (1964), 67-73. (with A. Radu)

7. Caractérisation des catégories abéliennes avec générateurs et limites inductives exactes, C. R. Acad. Sci. Paris 258 (1964), 4188-4191. (with Pierre Gabriel)

8. Asupra categoriilor preabeliene (On pre-Abelian categories), Stud. Cerc. Mat. Tom 17 (1965), 563–575 (with C. Bănică)

9. Sur les catégories preabéliens, Rev. Roumaine Math. Pures Appl., 10(1965), 621-633. (with C. Bănică)

10. La localisation pour des sites, Rev. Roumaine Math. Pures Appl. 10 (1965), 1031-1044.

11. Categorii cat (Quotient categories), Stud. Cerc. Mat. Tom 17, Nr. 6 (1965), 951-985. (with C. Bănică)

12. Sur la structure des objets de certaines catégories abéliennes, C.R. Acad. Sci. Paris, t. 262(1966), 1295-1297. (with C. Năstăsescu)

13. Elemente de teoria fasciculelor I, (Elements of the theory of sheaves, I), Stud. Cerc. Mat. (1966) 267-296.

14. Elemente de teoria fasciculelor II (Elements of the theory of sheaves, I), Stud. Cerc. Mat. (1966) 407-456.

15. Elemente de teoria fasciculelor III (Elements of the theory of sheaves, III), Stud. Cerc. Mat. (1966) 547-583.

16. Elemente de teoria fasciculelor IV (Elements of the theory of sheaves, IV), Stud. Cerc. Mat. (1966) 647-669.

17. Morphismes et co-morphismes des topos abéliens, Bull. Math. de la Soc. Sci. Math. de la R.S.R. Tom 10 (58) Nr. 4 (1966), 319-328. (with A. Radu)

18. Elemente de teoria fasciculelor V (Elements of the theory of sheaves, V), Stud. Cerc. Mat. (1966) 945-991.

19. Quelques observations sur les topes abéliens, Rev. Roumaine Math. Pures Appl. 12 (1967), 553-563. (with C. Năstăsescu)

20. Théorie générale de la décomposition, Rev. Roum Math. Pures et Appl. Tome XII, Nr. 9 (1967), 1365-1371.

21. Elemente de teoria fasciculelor VI (Elements of the theory of sheaves, VI), Stud. Cerc. Mat. (1967) 205-240.

22. Anneaux semi-artiniens, Bull. Soc. Math. France 96 (1968), 357-368. (with C. Năstăsescu).

23. Sur les epimorphismes plats d'anneaux, C.R. Acad. Sci. Paris 268 (1969), 376-379. (with T. Spîrcu).

24. On the localization ring of ring, J. Algebra 15 (1970), 41-56. (with C. Năstăsescu)

25. Quelques observations sur les Épimorphismes plats (à Gauche) d’Anneaux, J. Algebra Vol. 16, Nr.1 (1970), 40-59. (with T. Spircu)

26. Sur les quasi-ordres (à gauche) dans un anneau, J. Algebra 17, Nr. 4 (1971), 474-481. (with D. Spulber)

27. Les anneaux semi-noethériens, C.R. Acad. Sci. Paris t. 272 (1971), 1439-1441.

28. Le spectre à gauche d'un anneau, J. Algebra 18, No. 2 (1971), 213-228.

29. Sur les C. P. anneaux, C.R. Acad. Sci. Paris t. 272 (1971), 1493-1496.

30. Théorie primaire de la décomposition dans les anneaux semi-noethériens, J. Algebra Vol. 23, No. 3 (1972), 482-492.

31. Quelques considérations sur les anneaux semi-artiniens commutatifs, C. R. Acad. Sci. Paris t. 276 (1973), 1545-1548.

32. Some remarks about semi-Artinian rings, Rev. Roumaine Math. Pures Appl. Tome XVIII, Nr. 9 (1973), 1413-1422. (with C. Vraciu)

33. Exemple de inele semi-artiniene, (Examples of semi-Artinian rings), Stud. Cerc. Math. Tom 26, Nr. 8 (1974), 1153-1157. (with T. Spîrcu)

34. Permanence Theorems for semi-artinian rings, Rev. Roumaine Math. Pures Appl. XXI, Nr.2 (1976), 227-231. (with T. Spircu)

35. Sur l'anneau des quotients d'un anneau noethérien (à droite) par rapport au système localisant associe à un idéal bilatéral premier, C.R. Acad. Sci. Paris.

36. Sur la structure des anneaux absolument plats commutatifs, J. Algebra Vol. 40, No. 2 (1976), 364-383. (with C. Vraciu)

37. Some remarks about the regular ring associated to a commutative ring, Rev. Roumaine Math. Pures et Appl. Tome XXIII (1978), 269-277. (with C. Vraciu)

38. Sur la sous-catégorie localisante associée à un idéal bilatéral premier dans un anneau noethérien (à droite), Rev. Roumaine Math. Pures Appl. Tome XXVI, Nr. 7 (1981), 1033-1042.

39. Sur un problème d'Arens et Kaplansky concernant la structure de quelques anneaux absolument plats commutatifs, Rev. Roumaine Math. Pures Appl., Tome. XXVII, Nr. 8 (1982), 867-874. (with C. Vraciu)

40. Sur une classe de polynômes irréductibles, C.R. Acad. Sci. Paris, t. 297 (1983), 9-11.

41. On a class of Prüfer domains, Rev. Roum. Math. Pures et Appl. Tome XXIX, Nr. 9 (1984), 777-786.

42. Galois Theory of permitted extensions of commutative regular rings, Bull. Math. Soc. Sci. Math. R.S. Roumanie, Tome 29 (77), nr. 2 (1985), 121-135. (with C. Vraciu)

43. On Dedekind Domains in Infinite Algebraic Extensions, Rend. Sem. Mat. Univ. Padova, Vol. 74 (1985), 39-44. (with C. Vraciu)

44. Local class field theory. I, (Romanian, Teoria locală a corpului claselor. I,. English summary), Stud. Cerc. Mat. 37 (1985), no. 4, 295–312.

45. On subfields of k(x), Red. Sem. Mat. Univ. Padova, Vol. 75 (1986), 257-273. (with V. Alexandru)

46. Local class field theory. II. (Romanian, Teoria locală a corpului claselor. I), Stud. Cerc. Mat. Tom 38, (1986), No.2, 107-138.

47. On a problem of Nagata in valuation theory, Rev. Roumaine Math. Pures Appl. Tome XXXI, Nr. 7 (1986), 639-641.

48. On a class of intermediate Subfields, Stud. Cerc. Mat., Tom 39, Nr. 2 (1987), p. 156-162. (with E.L. Popescu)

49. Sur une clase de prolongements à K(X) d'une valuation sur un corps K, Rev. Roumaine Math. Pures Appl., Tome XXXIII (1988), 393-400. (with V. Alexandru)

50. A theorem of characterization of residual transcendental extensions of a valuation, J. Math. Kyoto Univ. Vol. 28, Nr. 4 (1988), 579-592. (with V. Alexandru and A. Zaharescu)

51. Sur la définition des prolongements résiduels transcendents d'une valuation sur un corps K à K(X), Bull. Math. Soc. Sci. Math. Roumanie, Tome. 33 (1989), 257-264. (with E. L. Popescu)

52. Minimal pairs of definition of a residual transcendental extension of a valuation, J. Math. Kyoto, Univ., Vol. 30, Nr. 2 (1990), 207-225. (with V. Alexandru and A. Zaharescu)

53. All valuations on K(X), J. Math. Kyoto Univ., Vol. 30, Nr. 2 (1990), 281-296. (with V. Alexandru and A. Zaharescu)

54. On the residual transcendental extensions of a valuation. Key polynomials and augmented valuation, Math. Tsukuba Univ. Vol. 15, No.1 (1991), 57-78. (with E.L. Popescu)

55. A characterization of Generalized-Dedekind Domains, Bull. Math. de la Soc. Sci. Math. de Roumanie, Tome 35 (83), Nr.1-2 (1991), 139-141. (with E. L. Popescu)

56. On the Extension of Valuations on a Field K to K(X) – I, Red. Sem. Mat. Univ. Padova, Vol. 87 (1992), 151-168. (with C. Vraciu) 57. Some elementary remarks about n-local fields, Rend. Sem. Math. Univ. Padova, Vol. 91 (1994), 17-28 (with V. Alexandru)

58. On a class of valuations on K(X), 11th National Conference of Algebra, Constanta, 1994, An. St. Univ. Ovidius Constantza, Seria: Mat. Vol. II (1994), 120-136. [53] (with A. Zaharescu)

59. Sur une classe d'anneaux qui généralisent les anneaux de Dedekind, J. Algebra, Vol.173, (1995), 44-66. (with M. Fontana)

60. On the structure of the irreducible polynomials over local fields, J. Number Theory, Vol. 52, No. 1 (1995), 98-118. (with A. Zaharescu)

61. Sur une classe d’anneaux de Prüfer avec groupe de classes de torsion, Comm. Algebra 23 (1995), no. 12, 4521–4533. (with M. Fontana)

62. Completion of r. t. extension of a local field (I), Math. Z., Vol. 221 (1996), 675-682. (with V. Alexandru and A. Popescu)

63. On the extension of a valuation on a Field K to K(X) - II, Rend. Sem. Mat, Univ. Padova, Vol. 96 (1996), 1-14. (with C. Vraciu)

64. On a class of Domains having Prüfer integral closure: The FQR-domains, Commutative ring theory (Fès, 1995), 303-312, Lecture Notes in Pure and Appl. Math. Vol. 185, Dekker, New York, 1997. (with M. Fontana)

65. On the main invariant of an element over a local field, Portugalia Mathematica, Vol. 54, Fasc. 1 (1997), 73-83. (with A. Zaharescu)

66. On the closed subfields of Cp, J. Number Theory, Vol. 68, No. 2 (1998), 131-150. (with V. Alexandru and A. Zaharescu)

67. The Lüroth's Theorem for some complete fields, in Abelian Groups, Module Theory and Topology, Editors Dikranian-Salce, Marcel Dekker Inc., 1998, 55-58. (with V. Alexandru)

68. Abelian groups, module theory, and topology (Padua, 1997), 55–58, Lecture Notes in Pure and Appl. Math., 201, Dekker, New York, 1998.

69. Completion of r. t. extensions of local fields (II), Rend. Sem. Mat. Univ. Padova, Vol. 100 (1998). (with V. Alexandru and A. Popescu)

70. On the roots of a class of lifting polynomials, Fachbereich Math. Univ. Hagen, Band 63 (1998), 586-600. (with A. Zaharescu)

71. Invertible ideals and Picard group of generalized Dedekind domains, J. Pure and Appl. Alg., Vol 135, Nr. 3 (1999), 237-251. (with S. Gabelli)

72. The generating degree of Cp, Canad. Math. Bull. Vol. 44 (1), 2001, 3-11. (with V. Alexandru and A. Zaharescu)

73. Trace on Cp, J. Number Theory 88 (2001), Nr.1, 13-48. (with V. Alexandru and A. Zaharescu)

74. Spectral norms on valued fields, Math. Z., Vol. 238 (2001), 101-114. (with V. Pasol and A. Popescu)

75. Metric invariants in B+dR associated to differential operators, Rev. Roumaine Math. Pures Appl. XLVI, Nr. 5 (2001), 552-564. (with V. Alexandru and A. Zaharescu)

76. Completion of the Spectral extensions of p-adic valuation, Rev. Roum. Math. Pures et Apll, Vol. XLVI, Nr. 6 (2001), 805-817. (with E. L. Popescu and C. Vraciu)

77. Nagata Transform and Localizing Systems, Comm. in Algebra, 30(5), (2002), 2297-2308. (with Marco Fontana)

78. Chains of metric invariants over a local field, Acta Arithmetica, 103.1 (2002), 27-40. (with A. Popescu, M. Vajaitu and A. Zaharescu)

79. Universal property of the Kaplansky ideal transform and affineness of Open Subsets, J. Pure and Appl. Alg., 173, (2002), 121-134. (with Marco Fontana)

80. Total valuation rings of K(X, σ) containing K, Communications in Algebra, Volume 30, Number 11 (2002), 5535 – 5546. (with S. Kobayashi, H. Marubayashi and C. Vraciu)

81. On minimal pairs and residually transcendental extensions of valuations (Mathematika, 49 (2002), 93-106. (with S. Khanduja and K.W. Roggenkamp)

82. Total valuation rings of Ore extensions, Result. Math., 43 (2003), 373-379. (with S. Kobayashi, H. Marubayashi, C. Vraciu and G. Xie)

83. Galois action on plane compacts, Proceedings of the 35th Symposium on Ring Theory and Representation Theory (Okayama, 2002), 113–120, Symp. Ring Theory Represent Theory Organ. Comm., Okayama, 2003.

84. Transcendental divisors and their critical functions, Manuscripta Math., 110 (4), (2003), 527-541. (with A. Popescu and A. Zaharescu)

85. Trace Series on Q ̃K, Result. Math., 43 (2003), 331-341 (with A. Popescu and A. Zaharescu)

86. Metric invariants over Henselian valued Fields, J. Algebra, 266 (1), (2003), 14-26. (with A. Popescu and A. Zaharescu)

87. Galois structures on plane compacts, J. Algebra, 270, (2003), 238-248. (with A. Popescu and A. Zaharescu)

88. Good elements and metric invariants in B+dR, J. Math. Kyoto Univ, vol 43, Nr. 1 (2003), 125-137. (with V. Alexandru and A. Zaharescu)

89. A representation theorem for a class of rigid analytic functions, J. Th. Nombres Bordeaux, 15 (2003), 639-650. (with V. Alexandru and A. Zaharescu)

90. A characterization of completion of the spectral extension of p-adic valuation, World Conference on 21st Century Mathematics 2004, 157–161, Sch. Math. Sci.G.C. Univ., Lahore, 2004. (with E. L Popescu)

91. On afine subdomains, Rev. Roum. Math. Pure Appl., XLIX, No. 3 (2004), 231-246 (with G. Groza)

92. A Galois theory for the Banach algebra of continuous symmetric functions on absolute Galois groups, Result. Math. 45, No. 3-4 (2004), 349-358. (with A. Popescu and A. Zaharescu)

93. On the continuity of the trace, Proceeding Romanian Academy, Series A, Volume 5, Number 2 (2004), 117-122. (with V. Alexandru and E. L Popescu)

94. Non-commutative valuation rings of the quotient artinian ring of a skew polynomial ring, Algebras and Representation Theory (2005), 8; 57-68 (with S. Kobayashi, H. Marubayashi, C. Vraciu and G. Xie)

95. A basis of C(X, Cp) over C(X, Qp), Rev. Roumaine Math. Pures Appl. Tome LI, Nr. 1 (2006), 87-88. (with E. L. Popescu)

96. On the structure of compact subsets of Cp, Acta Arithmetica, 123. 3 (2006), 253-266. (with A. D. R. Choudary, and A. Popescu)

97. On the existence of trace for elements of Cp, Algebras and Representation Theory (2006) 9: 47-66. (with M. Vajaitu and A. Zaharescu)

98. The p-adic measure on the orbit of an element of Cp, Rend. Sem. Mat. Univ. Padova, Vol.118 (2007), 197-216. (with V. Alexandru, M. Vajaitu and A. Zaharescu)

99. Analytic Normal Basis Theorem Cent. Eur. J. Math., 6 (3) (2008), 351-356. (with V. Alexandru and A. Zaharescu)

100. Norms on K[X1, . . . ,Xr], which are multiplicative on R, Result. Math., 51 (2008), 229-247. (with G. Groza and A. Zaharescu)

101. On the automorphisms of the spectral completion of the algebraic numbers field, Journal of Pure and Applied Algebra, 212 (2008), 1427–1431. (with E. L Popescu and A. Popescu)

102. All non–Archimedean norms on K[X1, . . . ,Xr], Glasg. Math. J. 52, (2010), No.1, 1-18 (with G. Groza and A. Zaharescu)

103. On the Iwasawa algebra associated to a normal element of Cp, Proc. Indian Acad. Sci. Math. Sci. 120, (2010), No. 1, 45-55. (with V. Alexandru, M. Vajaitu and A. Zaharescu)

104. A Galois Theory for the field extensions K((X))/ K, Glasg. Math. J. 52,(2010), 447-451 (with Asim Naseen and A. Popescu)

105. On the spectral norm of algebraic numbers (to appear in Math. Nachtr.) (with A. Popescu and A. Zaharescu)

106. The behavior of rigid analytic functions around orbits of elements of Cp (to appear) (with S. Achimescu, V. Alexandru, M. Vajaitu and A. Zaharescu)

107. On localizing systems in a Prüfer Domain (to appear in Communications in Algebra) (with H. Marubayashi and E.L. Popescu)

108. The study of the spectral p-adic extension (to appear in Proc. Rom. Acad.)

109. Some compact subsets of Qp (to appear in Rev. Roum. Math. Pures et Apll.)

110. Representation results for equivariant rigid analytic functions (to appear) (V. Alexandru, N. Popescu, M. Vajaitu and A. Zaharescu)

111. On the zeros of rigid analytic functions (to appear) (V. Alexandru, N. Popescu, M. Vajaitu and A. Zaharescu).

See also

Carol I High School

Notes

1. ^ http://codrinscutaru.blogspot.com/2010/08/matematica-pierdut-un-nume-nicolae.html
2. ^ http://planetmath.org/encyclopedia/AdjointFunctor.html
3. ^ Seminars on Algebraic Geometry and Category theory
4. ^ Nicolae Popescu. Abelian Categories with Applications to Rings and Modules, Academic Press, L. M. S. Monograph No.3, London, 1973.,ISBN 0-12-561550-7

External links

• Nicolae Popescu at the Mathematics Genealogy Project.
• Nicolae Popescu - Institute of Mathematics of the Romanian Academy
• Nicolae Popescu --Biography
• Nicolae Popescu at the Mathematics Genealogy Project.

Persondata
Name	Popescu, Nicolae
Alternative names
Short description
Date of birth	22 September 1937
Place of birth	Strehaia, Romania
Date of death	29 July 2010
Place of death	Bucharest