JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (11): 95-100.doi: 10.6040/j.issn.1671-9352.0.2023.476

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Strongly Gorenstein projective modules over Morita rings

XIA Xu, CHEN Wenjing*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2025-11-11

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Abstract: Let Λψ=(A NM B)(0,ψ) be a Morita ring with one bimodule homomorphism zero, where A and B are noetherian rings, N is an A-B-bimodule, M is a B-A-bimodule, and ψ:NBM→A is a homomorphism of A-A-bimodules. We give the sufficient condition that a Λψ-module is a strongly Gorenstein projective module.

Key words: Morita ring, strongly Gorenstein projective module, strongly complete projective resolution, weakly compatible module

CLC Number: 

  • O153.3
[1] AUSLANDER M, BRIDGER M. Stable module theory[M]. Providence: American Mathematical Society, 1969:94.
[2] ENOCHS E E, JENDA O M G. Gorenstein injective and projective modules[J]. Mathematische Zeitschrift, 1995, 220(4):611-633.
[3] ENOCHS E E, JENDA O M G. Relative homological algebra[M]. Berlin: Walter De Gruyter, 2000.
[4] HOLM H. Gorenstein homological dimensions[J]. Journal of Pure and Applied Algebra, 2004, 189(1/3):167-193.
[5] BENNIS D, MAHDOU N. Strongly Gorenstein projective, injective, and flat modules[J]. Journal of Pure and Applied Algebra, 2007, 210(2):437-445.
[6] BASS H. The Morita theorems, mimeographed notes[M]. Oregon: University of Oregon, 1962.
[7] GREEN E L. On the representation theory of rings in matrix form[J]. Pacific Journal of Mathematics, 1982, 100(1):123-138.
[8] GAO Nan, PSAROUDAKIS C. Gorenstein homological aspects of monomorphism categories via Morita rings[J]. Algebras and Representation Theory, 2017, 20(2):487-529.
[9] GUO Qianqian, XI Changchang. Gorenstein projective modules over rings of Morita contexts[J]. Science China Mathematics, 2023, 66, https://doi.org/10.1007/s11425-022-2206-8.
[10] GREEN E L, PSAROUDAKIS C. On Artin algebras arising from Morita contexts[J]. Algebras and Representation Theory, 2014, 17(5):1485-1525.
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