Nicolae Popescu

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NICOLAE POPESCU (born 22 September 1937, Strehaia, Romania) is a Romanian mathematician, best known for his contributions to algebra.

During his career he has published 98 papers and 6 books. He is married, has three children. He earned his MS in Mathematics in 1964, and his Ph.D. in the same subject in 1967, both at the University of Bucharest. He lectured at the University of Bucharest from 1968 to 1972. Since 1964, he has held a research professorship position at the Institute of Mathematics of the Romanian Academy.

His areas of expertise are Category theory, Abelian Categories with Applications to Rings and Modules, Theory of Rings, Fields and Polynomials, and Valuation Theory; with further interest in Algebraic Topology, Algebraic Geometry, Commutative Algebra, K-Theory, Class-Field theory, and Algebraic Function Theory.

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[edit] PUBLICATIONS

  1. Asupra omologiei si omotopiei C.W. - complexelor, Studii si cercetari Mat., 1962. (with D. Burghelea)
  2. Diferentiale generalizate, Comunicarile Acad. R.S.R., Vol. 13, Nr. 6 (1963), 523-528. (with C. Banica)
  3. Module cu diferentiala generalizata, St. Cerc. Mat. Tom. 16 Nr. 6. (1964), 673-804.
  4. Modules avec différentielle généralisée Rev. Roum. Math. Pures et Appl. Nr. 6 (1964)
  5. Quelques considérations sur l'exactitude des foncteurs, Bull. Math. Soc. Sci. Math. Phis. de la R. P. R. 7 (1963), 144-147. (with C. Banica)
  6. Categorii cât, St. Cerc. Mat. 17 (1965), 951-985. (with C. Banica)
  7. Sur les catégories preabéliens, Rev. Roum. Math. Pures Appl., 10(1965), 621-633. (with C. Banica)
  8. Caractérisation des catégories abéliennes avec générateurs et limites inductives exactes, C. R. Acad. Sci. Paris 258(1964), 4188-4191. (with Pierre Gabriel)
  9. La localisation pour des sites, Rev. Roum. Math. Pures et Appl. 10(1965), 1031-1044.
  10. 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)
  11. Morphismes et co-morphismes des topos abéliens, Bull. Math. de la Soc. Sci. Math. de la R.S.R. Tom 10(58) W 2 =4 (1996), 319-328. (with A. Radu)
  12. Elemente de teoria fascicolelor I, St. Cerc. Mat. (1966) 267-296.
  13. Elemente de teoria fascicolelor II, St. Cerc. Mat. (1966) 407-456.
  14. Elemente de teoria fascicolelor III, St. Cerc. Mat. (1966) 547-583.
  15. Elemente de teoria fascicolelor IV, St. Cerc. Mat. (1966) 647-669.
  16. Elemente de teoria fascicolelor V, St. Cerc. Mat. (1966) 945-991.
  17. Elemente de teoria fascicolelor VI, St. Cerc. Mat. (1967) 205-240.
  18. Sur la structure des objets de certaines catégories abéliennes, C.R. Acad. Sci. Paris 262(1966), 1295-1297. (with C. Nastasescu)
  19. Quelques observations sur les topes abéliens, Rev. Roum. Math. Pures Appl.12 (1967), 553-563. (with C. Nastasescu)
  20. Théorie générale de la décomposition, Rev. Roum Math. Pures et Appl. 12 (1967), 1365-1371.
  21. Les anneaux semi-artiniens, Bull. Soc. Math. France 96 (1968) 357-368. (with C. Nastasescu).
  22. Sur les epimorphismes plants d'anneaux, C.R. Acad. Sci. Paris 268 (1969) 376-379. (with T. Spircu).
  23. On the localization ring of ring, J. of Algebra 15 (1970) 41-56. (with C. Nastasescu)
  24. Quelques observations sur les morphismes plats des anneaux, J. Algebra 16(1970), 40-59. (with T. Spircu)
  25. Le spectre gauche d'un anneau, J. Algebra 18(1971) 213-228.
  26. Les quasi-ordres (á gauche) des anneaux, J. Algebra 17(1971), 474-481. (with D. Spulber)
  27. Les anneaux semi-noethériens, C.R. Acad. Sci. Paris 272 (1971), 1439-1441.
  28. Sur les C. P. anneaux, C.R. Acad. Sci. Paris 272 (1971) 1493-1496.
  29. Théorie de la décomposition primaire dans les anneaux semi-noethériens, J. Algebre 2399172), 482-492.
  30. Some remarks about semi-artinian rings, Rev. Roumaine Math. Pures et Appl. 17, nr. 9(1973), 1413-1422. (with C. Vraciu)
  31. Exemple de inele semi-artiniene, St. Cerc. Math. 26, nr.8 (1974), 1153-1157. (with T. Spircu)
  32. Quelques considérations sur les anneaux semi-artiniens commutatifs, C. R. Acad. Sci. Paris 276(1973), 1545-1548.
  33. Permanence Theorems for semi-artinian rings, Rev. Roum. Math. Pures et Appl. 21, nr.2 (1976), 227-231. (with T. Spircu)
  34. Sur la Structure des Anneaux Absolument plats commutatifs, J. Algebra 40 (1976), 364-383. (with C. Vraciu)
  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. Some remarks about the regular ring associated to a commutative ring, Rev. Roumaine Math. Pures et Appl. 23(1978), 269-277. (with C. Vraciu)
  37. Sur la sous-catégorie localisant associée a un idéal bilatéral premier dans un anneau noethérien (à droite), Rev. Roum. Math. Pures et Appl. T. XXVi, nr. 7 (1981), 1033-1042.
  38. Sur un problème d'Arens et Kaplansky concernant la structure de quelques anneaux absolument plats commutatifs, Rev. Roum. Math. Pures Appl., t. 27, nr.8 (1982), 867-874. (with C. Vraciu)
  39. Sur une classe de polynômes irréductibles, C.R. Acad. Sci. Paris, t. 297 (1983), 9-11.
  40. Galois Theory of permitted extensions of commutative regular rings, Bull. Math. Soc. Sci. Math. R.S. Roumanie, t. 29 (77), nr.1 (1985), 121-135. (with C. Vraciu)
  41. On Dedekind domains in infinite algebraic extensions, Rend. Sem. Math. Univ. Padova, vol. 74 (1985), 39-44. (with C. Vraciu)
  42. On a problem of Nagata in valuation theory, Rev. Roum. Math. Pures et Appl. 31 (1986), 639-641.
  43. On subfields of k(X), Red. Sem. Mat. Univ. Padova, vol. 75 (1986), 257-273. (with V. Alexandru)
  44. On a class of intermediate Subfields, Studii si Cercetari Matematice, tom 39, Nr. 2 (1987), p.156-162. (with E.L. Popescu)
  45. Sur une clase de prolongements a K(X) d'une valuation sur un corps K, Rev. Roum. Math. Pures Appl. 33 (1988), 393-400. (with V. Alexandru)
  46. A theorem of characterization of residual transcendental extensions of a valuation, J. Math. Kyoto Univ. 28-4 (1988), 579-592. (with V. Alexandru and A. Zaharescu)
  47. Sur la définition des prolongements résiduels transcendent d'une valuation sur un corps K à K(X), Bull. Math. Soc. Sci. Math. Roumanie, t. 33 (1989), 257-264. (with E. L. Popescu)
  48. Minimal pairs of a residual transcendental extension of a valuation, J. Math. Kyoto, Univ., Vol. 30, (1990), 207-225. (with V. Alexandru si A. Zaharescu)
  49. All valuations on K(X), J. Math. Kyoto Univ., Vol. 30 (1990), 281-296. (with V. Alexandru si A. Zaharescu)
  50. 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)
  51. On the extension of valuation on a field K to K(X), I Red. Sem. Mat. Univ. Padova, vol. 87 (1992), 151-168. (with C. Vraciu)
  52. On the structure of the irreducible polynomials over local fields, J. Number Theory, Vol. 52 No.1 (1993), 98-118. (with A. Zaharescu)
  53. The valuations on k(x,y) which are trivial on k, Proc. Conf. Algebra, Constanta, 1994.
  54. Some elementary remarks about n-local fields, Rend. Sem. Math. Univ. Padova, Vol. 91 (1994). (with V. Alexandru)
  55. A characterization of Generalized Dedekind Domains, Bull. Math. de la Soc. Sci. Math de la Roumanie, tome 35 (83), Nr.1-2 (1991), 139-141. (with E. L. Popescu)
  56. On a class of Prüfer domains, Rev. Roumaine Math. Pures et Appl. 29 (1984), 777-786.
  57. Sur une classe d'anneaux qui généralisent les anneaux de Dedekind, J. of Algebra, Vol.173, (1995), 44-66. (with M. Fontana)
  58. 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)
  59. On the roots of a class of lifting polynomials, Fachbereich Math. Univ. Hagen, Band 63 (1998), 586-600. (with A. Zaharescu)
  60. Completion of a r. t. extension of a local field, I, Math. Z., Vol 221 (1996), 675-682. (with V. Alexandru and A. Popescu)
  61. Completion of a r. t. extension of a local field”, II, Rend. Sem. Mat. Univ. Padova, (1998). (with V. Alexandru and A. Popescu)
  62. On the main invariant of an element over a local field, Portugalia Mathematica, Vol. 54, Fasc. 1 (1997) 73-83. (with A. Zaharescu)
  63. On the closed subfields of Cp, J. Number Theory, Vol. 68 (1997), 131-150. (with V. Alexandru and A. Zaharescu)
  64. Sur une classe d'anneaux de Prüfer avec groupe de classes de torsion, Comm. Alg., 23 (1975), 4521-4533. (with M. Fontana)
  65. On a class of Domains Having Prüfer Integral closure, The FOR-Domains, Commutative ring Theory, Vol. 185, Lecture Notes in Pure and Appl. Math. Dekker 1996. (with M. Fontana)
  66. Invertible ideals and Picard group of generalized Dedekind domains, J. Pure and Appl. Alg., Vol 135, Nr. 3 (1999), 237-251. (with S. Gabelli)
  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. On minimal pairs and residually transcendental extensions of valuations (Mathematika, 49(2002), 93-106 ) (with S. Khanduja and K.W. Roggenkamp)
  69. Nagata Transform and Localizing Systems, Comm. in Algebra, 30(5), (2002), 2297-2308. (with Marco Fontana)
  70. Spectral extensions of p-adic valuation, Rev. Roum. Math. Pures et Apll, Vol. 46, Nr.6 (2001), 805-817. (with E. L. Popescu and C. Vraciu)
  71. Trace on Cp, J. Number Theory 88 (2001), Nr.1, 13-48. (with V. Alexandru and A. Zaharescu)
  72. Spectral norms on valued fields, Math. Z., Vol 238 (2001), 101-114. (with V. Pasol and A. Popescu)
  73. The generating degree of Cp, Canad. Math. Bull. Vol. 44, (2001), 3-11. (with V. Alexandru and A. Zaharescu)
  74. Metric invariants in BdR+ associated to differential operators, Rev. Roum. Math. Pures Appl. 33 (1988), 393-400. (with V. Alexandru and A. Zaharescu)
  75. Good elements and metric invariants in BdR+, J. Math. Kyoto Univ, vol 43, Nr. 1 (2003), 125-137. (with V. Alexandru and A. Zaharescu)
  76. On afine subdomains (to appear) (with G. Groza)
  77. A representation theorem for a class of rigid analytic functions, (with V. Alexandru and A. Zaharescu) (J. Th. Nombres Bordeaux 15 (2003), 639-650.
  78. On the spectral norm of Algebraic Numbers (to appear Math. Nachtr.) (with A. Popescu and A. Zaharescu)
  79. Universal Property of the Kaplansky Ideal Transform and Affiness of Open Subsets, J. Pure and Appl. Alg., 173, (2002), 121-134. (with Marco Fontana)
  80. Metric invariants over Henselian valued Fields, J. Of Algebra, 266 (1), (2003), 14-26. (with A. Popescu and A. Zaharescu)
  81. Chains of metric invariants over a local field, Acta Arithmetica, 103 (1), (2002), 27-40. (with A. Popescu, M. Vajaitu and A. Zaharescu)
  82. Transcendental divisors and their critical functions, Manuscripta Math., 110 (4), (2003), 527-541. (with A. Popescu and A. Zaharescu)
  83. The Galois Action on plane Compacts, J. Of Algebra, 270, (2003), 238-248. (with A. Popescu and A. Zaharescu)
  84. 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)
  85. Total valuation Rings of Ore extensions, Result Math., 43 (2003), 373-379. (with S. Kobayashi, H. Marubayashi and C. Vraciu and G. Xie)
  86. Non-commutative valuation rings of the quotient artinian ring of a skew polynomial ring, Algebra and Representation Theory (2005), 8; 57-68 (with S. Kobayashi, H. Marubayashi and C. Vraciu and G. Xie)
  87. The structure of localization systems of a class of Prüfer Domain (to appear) (with H. Marubayashi and E. L Popescu)
  88. On the existence of trace for elements of Cp Algebra and Representation Theory (2006), 9; 47-66 (with M. Vajaitu and A. Zaharescu)
  89. Trace Series on Qk, Result in Math., 43 (2003), Nr 3-4, 331-341 (with A. Popescu and A. Zaharescu)
  90. A Galois Theory for the Banach Algebra of continuous symmetric functions on absolute Galois Group Result. Math. 45, No. 3-4, 349-358 (2004) (with A. Popescu and A. Zaharescu)
  91. On the continuity of the trace (Proceeding Romanian Academy, Series A, Volume 5, Number 2 (2004), 117-122 (with V. Alexandru, E. L Popescu)
  92. A new characterization of spectral extension of p-adic valuation, Proc. Conference in Math. Lahore, 18-20 mars 2004 (with E. L Popescu)
  93. Norms on R[X1, ...., Xr] which are multiplicative von R (to appear in Resultate der Mathematik (with G. Groza and A. Zaharescu)
  94. All non–archimedean norms on K[X1, ...., Xr] (to appear) (with G. Groza and A. Zaharescu)
  95. On the structure of compact subsets of Cp (Acta Arithmetica, 123. 3, 253-266 (2006) (with Alla Ditta Raza Choudary, and A. Popescu)
  96. A basis of over, Rev. Roum. Math. Pures Appl. Tome LI, 51 (2006), 87-88. (with E. L. Popescu)
  97. The p-adic measure on the orbit of an element of Cp (to appear) (with V. Alexandru, M. Vajaitu and A. Zaharescu)
  98. Analytic Normal Basis Theorem (with V. Alexandru and A. Zaharescu) (to appear)

BOOKS

  1. Elemente de teoria analitica a numerelor, Univ. Bucuresti, 1968.
  2. Teoria categoriilor si teoria fascicolelor, Ed. Stiintifica, 1971.
  3. Categorii Abeliene, Ed. Academiei, 1971.
  4. Abelian categories with Applications to Rings and Modules, Academic Press, L. M. S. Monograph No.3, London, 1973.
  5. Theory of Categories, Editura Academiei R.S.R and Sijthoff et Noordhoff, Olanda, 1979. (with E. L. Popescu).
  6. Selected topics in valuation theory (to appear).

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