Strongly Gorenstein graded modules

Abstract

Let R be a graded ring. We define and study strongly Gorenstein gr-projective, gr-injective, and gr-flat modules. Some connections among these modules are discussed. We also explore the relations between the graded and the ungraded strongly Gorenstein modules.

Keywords

Strongly Gorenstein gr-projective module / strongly Gorenstein gr-injective module / strongly Gorenstein gr-flat module

References

[1] Asensio M J, Lopez Ramos J A, Torrecillas B. Gorenstein gr-injective and gr-projective modules. Comm Algebra, 1998, 26: 225–240

[2] Asensio M J, Lopez Ramos J A, Torrecillas B. Gorenstein gr-flat modules. Comm Algebra, 1998, 26: 3195–3209

[3] Asensio M J, Lopez Ramos J A, Torrecillas B. FP-gr-injective modules and gr-FC rings. Lect Notes Pure Appl Math, 2000, 1–12

[4] Auslander M, Bridger M. Stable Module Theory. Mem Amer Math Soc, No 94. Providence: Amer Math Soc, 1969

[5] Bennis D, Mahdou N. Strongly Gorenstein projective, injective and flat modules. J Pure Appl Algebra, 2007, 210: 437–445

[6] Ding N Q, Chen J L. The flat dimensions of injective modules. Manuscripta Math, 1993, 78: 165–177

[7] Ding N Q, Chen J L. Coherent rings with finite self-FP-injective dimension. Comm Algebra, 1996, 24: 2963–2980

[8] Enochs E E, Jenda O M G. Gorenstein injective and Gorenstein projective modules. Math Z, 1995, 220: 611–633

[9] Enochs E E, Jenda O M G. Relative Homological Algebra. Berlin: Walter de Gruyter, 2000

[10] Enochs E E, Jenda O M G, Torrecillas B. Gorenstein flat modules. Nanjing Univ J Math Biquarterly, 1993, 10: 1–9

[11] Enochs E E, Lóopez-Ramos J A. Gorenstein Flat Modules. New York: Nova Science Publishers, Inc, 2001

[12] Garcíıa Rozas J R, Ĺopez-Ramos J A, Torrecillas B. On the existence of flat covers in R-gr. Comm Algebra, 2001, 29: 3341–3349

[13] Hermann M, Ikeda S, Orbanz U. Equimultiplicity and Blowing Up. New York: Springer, 1988

[14] Nastasescu C, Raianu S, Van Oystaeyen F. Modules graded by G-sets. Math Z, 1990, 203: 605–627

[15] Nastasescu C, Van Oystaeyen F. Graded Ring Theory. North-Holland Math Library, Vol 28. Amsterdam: North-Holland, 1982

[16] Nastasescu C, Van Oystaeyen F. Methods of Graded Rings. Lecture Notes in Math, Vol 1836. Berlin: Springer-Verlag, 2004

[17] Rotman J J. An Introduction to Homological Algebra. New York: Academic Press, 1979

[18] Stenstr�om B. Rings of Quotients. Berlin: Springer-Verlag, 1975

[19] Yang X Y, Liu Z K. Strongly Gorenstein projective, injective and flat modules. J Algebra, 2008, 320: 2659–2674

[20] Yang X Y, Liu Z K. FP-gr-injective modules. Math J Okayama Univ, 2011, 53: 83–100

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Higher Education Press and Springer-Verlag Berlin Heidelberg