Dorin Popescu

Email: d_popescu@sms.edu.pk

Course: Algebra

Publications

1. Quelques applications de la decomposition triangulaire, Publ. Dept. Math. Lyon
3-4 (1967), 63-68.
2. On the algebraic categories (with G.Georgescu), Rev Roum. Math.Pures et Appl.,
13(1968),337-342.
3. Les faisceaux d’une theorie, C.R.Acad. Sc.Paris ,269(1969),380-382.
4. Sur les categories des (t,T)-faisceaux, C.R.Acad.Sc.Paris,269(1969), 413-415.
5. Deux extensions des ensembles preordonnes (with N.Manolache), Rev.Roum.
Math.Pures et Appl.,15(1970),569-572.
6. Some remarks on complete cogenerated categories, Rev.Roum.Math.Pures et
Appl.,15(1970), 1027-1033.
7. Monoconuri proiective si epiconuri inductive (in Romanian), Std. Cerc. Mat., 22
(1970), 641-647.
8. Categories de faisceaux, Journal of Algebra,18(1971),343-365.
9. Les faisceaux d’une classe des morphismes, C.R. Acad.Sc.Paris, 272(1971), 101-103.
10. Cofaisceaux d’une categorie, C.R. Acad.Sc.Paris, 272(1971),299-302.
11. A strong approximation theorem over discrete valuation rings, Rev. Roum. Math.
Pures et Appl., 20(1975), 659-692.
12. Die strenge Approximationseigenschaft lokaler Ringe (with G.Pfister), Inventiones
Math. 30(1975),145-174.
13. Some algorithmic methods in the theory of local complete rings, Bull.Math. de la
Soc. Math. de la Roumaine,22(70)no.1(1978),61-69.
14. Algebraically pure morphisms, Rev.Roum.Math.Pures et Appl.,24(1979), 947-977.
15. Die Approximation von Primidealen (with G.Pfister), Bull. de l’Acad. Polonaise
Sci.,27(1979), 771-778.
16. A remark on two-dimensional local rings with the property of approximation,
Math.Z.,173(1980), 235-240.
17. Approximation properties and existential completeness for ring morphisms (with
S.Basarab, V.Nica), Manuscripta Math. 33(1981), 227-282.
18. On three dimensional local rings with the property of approximation (with G.Pfister),
Rev.Roum.Math.Pures et Appl., 26(1981),301-307.
19. Some extensions of Neron’s p-desingularization and approximation (with M.Cipu),
Rev.Roum.Math.Pures et Appl.,26(1981),1299-1304.
20. Global form of Neron’s p-desingularization and approximation, Proceedings ”Week
of Algebraic Geometry”, Bucharest,June 30-July 6(1980), Teubner Texte Band 40,Leipzig
1981.
21. On Zariski’s Uniformization Theorem, in Algebraic Geometry, Bucharest 1982,
Proceedings, Springer Lect.Notes in Math., 1056, Berlin,1984.
22. Ultraproducts and big Cohen-Macaulay modules (with C.Mateescu),Std. Cerc.
Mat.,36(1984), 424-428.
23. A desingularization theorem of Neron type (with M.Cipu), Ann.Univ. Ferrara,
30(1984), 63-76.
24. General Neron desingularization, Nagoya Math. J.,100(1985), 97-126.
25. A structure theorem on formally smooth morphisms in positive characteristic
(with V.Nica), Journal of Algebra,100(1986), 436-455.
26. Some structure theorems for valuation rings, Rev. Roum. Math. Pures et Appl.
31(1986), 577-582.
27. General Neron desingularization and Approximation, Nagoya Math. J., 104
(1986), 85-115.
28. Artin approximation theory and applications, Analele St. ale Univ. Iasi, 31(1985
supliment),11-14.
29. A certain desingularization Theorem (with M.Cipu),Analele St. ale Univ. Iasi,
31(1985 supliment),20-22.
30. Ultraproducts and Hochster’s modifications (with C.Mateescu), Analele St. ale
Univ. Iasi, 31(1985 supliment),26-27.
31. On the structure of formally smooth morphisms (with V.Nica), Analele St. ale
Univ. Iasi, 31(1985 supliment),33-34.
32. Algebraic extensions of valued fields, Journal of Algebra, 108(1987), 513-533.
33. Algebrization of deformations of exceptional couples (with M.Roczen), Rev.
Roum.Math. Pure et Appl.,33(1988),251-260.
34. Polynomial rings and their projective modules, Nagoya Math. J.,113(1989) ,121-
128.
35. Flatness in non-Noetherian ring theory, Rev.Roum.Math.Pures et Appl.,34(1989),
839-854.
36. Immediate extensions of filtered rings (with W.Morariu), Annali di Ferrara,
35(1989),35-57.
37. Indecomposable Cohen-Macaulay modules and the Brauer-Thrall Conjectures,
Proceedings of the Algebra Conference 9-10 June 1988, Brasov.
38. Indecomposable Cohen-Macaulay modules and irreducible maps (with M.Roczen)
, Compositio Math. 76(1990), 277-294.
39. Letter to the Editor, General Neron desingularization and approximation, Nagoya
Math. J.,118(1990),45-53.
40. Indecomposable Cohen-Macaulay modules and their multiplicities, Trans., AMS.,
323 (1991), 369-387.
41. The second Brauer-Thrall conjecture (with M.Roczen), Manuscripta Math. 71
(1991), 375-383.
42. Liftings of finite injective dimension modules, Analele Univ.Bucuresti, XL(1991),
65-75.
43. Indecomposable generalized Cohen-Macaulay modules (with M.Cipu, J.Herzog) ,
Trans AMS ,342(1994),107-136.
44. Relative liftings ,J of pure and Appl Alg., 108,n 3(1996).
45. Maximal Cohen-Macaulay modules over isolated singularities, Journal of Algebra,
178(1995), 710-732.
46. Deformations of maximal Cohen-Macaulay modules (with G.Pfister),Math.Z.,
223(1996),309-332
47. Maximal Cohen-Macaulay modules and their deformations, Analele Stiintifice
Constanta, v II(1994), 112-119.
48. Thom-Sebastiani problems for maximal Cohen-Macaulay modules(with J.Herzog),
Math.Ann., 309(1997),677-700.
49. Infinitesimal module deformations in the Thom-Sebastiani problem, (with F.
Enescu and G.Pfister),Archiv der Math. 69, 1997,196-208.
50. Hibert functions and generic forms (with J.Herzog), Compositio Math. 113
(1998),1-22.
51. Maximal Cohen-Macaulay modules over singularities of type Xt + Y 3 (with
B.Martin and G.Pfister), Revue Roum. Math. Pures et Appl.,42, no 7-8 (1997), 591-
619.
52. Special Cohen-Macaulay modules over singularities of type X3r + Y 3, Analele
Stiintifice Constanta,5 (2) (1997),112-119.
53. A family of Cohen-Macaulay modules over singularities of type Xt + Y 3, (with
G.Pfister), Commun. in Alg., 27(6)(1999), 2555-2572.
54. Variations on Green Theorem concerning the Hilbert functions, in: “Commutative
Algebra and Algebraic Geometry” editor F.Van Oystaeyen, Dekker Lect. Notes in Pure
and Appl. Math. 206(1999), 237-244.
55. Steps in the classification of Cohen-Macaulay modules over singularities of type
Xt + Y 3 (with V. Ene), Algebras and Representation Theory,vol 2, no 2 (1999), 137-175.
56. Free resolutions for deformations of maximal Cohen-Macaulay modules, (with L.
O’Carroll), Commun. in Alg., 28(11) (2000), 5329-5352.
57. On a Theorem of Kn¨orrer concerning Cohen-Macaulay modules, (with L.
O’Carroll), J. of Pure and Appl. Alg., (2000)
58. Betti numbers for p-stable ideals (with V.Ene and G.Pfister), Commun. in Alg.,
28(3),(2000), 1515-1531.
59. Combinatorics in Algebra and Geometry, Italian Journal of Pure and Appl Math.,
no 7(2000), 27-32.
60. Variations on N´eron desingularization, in: Sitzungsberichte der Berliner Mathematischen
Gesselschaft, Berlin, 2001, 143-151.
61. Splitting syzygies (with L. O’Carroll), Journal of Algebra, 228(2000),682-709.
62. On the regularity of p-Borel ideals (with J.Herzog), Proceedings of Amer. Math.
Soc., 129(2001), 2563-2570.
63. Betti numbers and the regularity of p-Borel ideals, Bul. St. Univ. Pitesti, Ser.
Mat.Inf., 5(2001),1-7.
64. Regularity of Rees algebras (with J.Herzog and N.V.Trung), J. London Math.
Soc., (2) 65, (2002), 320-338.
65. Explicit linear minimal free resolutions over a natural class of Rees algebras (with
J.Herzog and L. O’Carroll), Archiv Math., 2004.
66. Maximal Cohen-Macaulay modules over Y 3
1 + . . . + Y 3
n with few generators (with
R.Laza and L.O’Carroll), Math. Reports 3(53),2, (2001), 177-185.
67. Cohen-Macaulay representation, in Algebra-Representation Theory, Eds. K.W.
Roggenkamp and M. Stefanescu, Kluwer, 2001, p. 249-256.
68. Maximal Cohen-Macaulay modules over the cone of an elliptic curve (with R.
Laza, G. Pfister), Journal of Algebra, 253, (2002), 209-236.
69. Gr¨obner basis and depth of Rees algebras, Anal. Univ. Ovidius, Constanta, IX,
(2001), 81-88.
70. On the Ext-modules of ideals of Borel type (with J. Herzog, M. Vladoiu), in
Commutative Algebra, Interactions with Algebraic Geometry, Eds: L. Avramov et al,
Contemporary Math. Nr 331, AMS, Providence, 2003, 171-186.
71. Rank one maximal Cohen-Macaulay modules over singularities of type Y 3
1 + Y 3_2 + Y 3_ 3 + Y 3, 4 (with V. Ene), in Commutative Algebra, Singularities and Computer
Algebra, Eds: J. Herzog, V. Vuletescu, NATO Science Series, Vol 115, Kluwer Acad.
Publ.,Dordrecht-Boston-London, 2003, 141-157.
72. Rank two maximal Cohen-Macaulay modules over singularities of type Y 3
1 +Y 3, 2 +, Y 3, 3 + Y 3, 4 (with C. Baciu, V. Ene, G. Pfister), Prepr. 338, 2004, Kaiserslautern, accepted
for publication in Journal of Algebra.
73. On a question of Quillen, Bull. Math. Soc. Sci. Roum., Vol 45(93), no. 3-4
(2002), 209-212.
74. Finite filtrations of modules and shellable multicomplexes, (with J. Herzog), IMAR
Preprint no 4, 2005, Bucharest.
75. Extremal Betti numbers and regularity of Borel type ideals, Bull Math. Soc. Sc.
Roum. Vol 48(96), no 1,(2005)65-72.
76. Criterions for shellable multicomplexes,arXiv:math.AC/0505655, to appear in Annalele
Univ. Constanta.
77. Monomial cyclic basis of Koszul homology modules,arXiv:math.AC/0505656, submitted
to Communcations in Alg.
78. The strong Lefschetz property and simple extensions, (with J. Herzog), Preprint
Essen, June 2005.
Monographs and textbooks.
1. Die Approximationseigenschaft lokaler Ringe (with H. Kurke, T. Mostowski,
G.Pfister, M.Roczen), Lect. Notes in Math. 634(1978), Springer ,Berlin.
2. Henselian rings and Artin approximation property(in Romanian),(with V.Nica),
Univ Bucharest Press ,1979.
3. Elements of finite group theory (in Romanian),(with C.Vraciu) Ed. Stiintifica
Enciclopedica, Bucharest, 1986.
4. Artin approximation, in Handbook of Algebra, vol. 2, Ed. M.Hazewinkel, 2000
Elsevier Science, 321-356.
5. Artin Approximation, in Encyclopaedia of Mathematics, Suplement II, Ed. M.
Hazewinkel, Kluwer Academic Publishers, 2000, 30-32.
6. Cohen-Macaulay rings (in Romanian), in Seminar on Cohen-Macaulay rings and
modules, Ed. M. Stefanescu, Tip. Univ. of Iasi, 1986, Cap.IV.
7. Cohen-Macaulay modules and homological conjectures (in Romanian), in Actual
problems of mathematical research, Tip. Univ. of Bucharest, 1992, 101-113.
8. Bounds for Betti numbers, in Combinatorics in Algebra and Geometry, Sem. Ser.
in Math. Algebra: 2, Tip. Univ. Ovidius of Constanta, 1998, 65-70.
9. F-rational and strong F-rational rings, in Tight closure, Tip. Univ. Ovidius of
Constanta, 2001.