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A GENERALIZATION OF STRONGLY GORENSTEIN PROJECTIVE MODULES

Department of Mathematics, Faculty of Science and Technology of Fez, Box 2202, University S. M. Ben Abdellah Fez, Morocco

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and

NAJIB MAHDOU

Department of Mathematics, Faculty of Science and Technology of Fez, Box 2202, University S. M. Ben Abdellah Fez, Morocco

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https://doi.org/10.1142/S021949880900328XCited by:16 (Source: Crossref)

Abstract

This paper generalize the idea of the authors in J. Pure Appl. Algebra210 (2007) 437–445. Namely, we define and study a particular case of Gorenstein projective modules. We investigate some change of rings results for this new kind of modules. Examples over not necessarily Noetherian rings are given.

Keywords:

AMSC: 13D05, 13D07, 16E05, 16E10, 16E30

References

M. Auslander, Anneaux de Gorenstein et torsion en algèbre commutative, Secrétariat mathématique, Paris, 1967, Séminaire d'algèbre commutative dirigé par Pierre Samuel, 1966/67. Texte rédigé, d'après des exposés de Maurice Auslander, par Marquerite Mangeney, Christian Peskine et Lucien Szpiro, Ecole Normale Superieure de Jeunes Filles . Google Scholar
M. Auslander and M. Bridger , Memoirs. Amer. Math. Soc. 94 ( American Mathematical Society , Providence, Rhode Island , 1969 ) . Google Scholar
D. Bennis and N. Mahdou, J. Pure Appl. Algebra 210, 437 (2007), DOI: 10.1016/j.jpaa.2006.10.010. Crossref, Web of Science, Google Scholar
D. J. Benson and K. R. Goodearl, Pacific J. Math. 196, 45 (2000). Crossref, Web of Science, Google Scholar
H. Cartan and S. Eilenberg , Homological Algebra , Princeton Mathematical Series 19 ( Princeton University Press , Princeton , 1956 ) . Google Scholar
L. W. Christensen , Gorenstein Dimensions , Lecture Notes in Math. 1747 ( Springer–Verlag , Berlin, Heidelberg , 2000 ) . Crossref, Google Scholar
L. W. Christensen, A. Frankild and H. Holm, J. Algebra 302, 231 (2006), DOI: 10.1016/j.jalgebra.2005.12.007. Crossref, Web of Science, Google Scholar
E. E. Enochs and O. M. G. Jenda , Relative Homological Algebra , de Gruyter Expositions in Mathematics 30 ( Walter de Gruyter & Co. , Berlin , 2000 ) . Crossref, Google Scholar
E. Enochs and O. Jenda, Math. Z. 220, 611 (1995), DOI: 10.1007/BF02572634. Crossref, Web of Science, Google Scholar
E. E. Enochs and O. M. G. Jenda, Comm. Algebra 21, 3489 (1993), DOI: 10.1080/00927879308824744. Crossref, Web of Science, Google Scholar
E. Enochs, O. Jenda and B. Torrecillas, Nanjing Daxue Xuebao Shuxue Bannian Kan 10, 1 (1993). Google Scholar
E. Enochs, O. Jenda and J. Xu, Trans. Amer. Math. Soc. 348, 3223 (1996), DOI: 10.1090/S0002-9947-96-01624-8. Crossref, Web of Science, Google Scholar
H. Holm, J. Pure Appl. Algebra 189, 167 (2004), DOI: 10.1016/j.jpaa.2003.11.007. Crossref, Web of Science, Google Scholar
J. J. Rotman , An Introduction to Homological Algebra ( Academic Press , London, New York , 1979 ) . Google Scholar