JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (4): 9-15.doi: 10.6040/j.issn.1671-9352.0.2022.619

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Gorenstein FP-injective modules over Morita rings

Wenjing CHEN(),Wen GAO   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2022-11-28 Online:2024-04-20 Published:2024-04-12

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Abstract:

The method of constructing Gorenstein FP-injective modules on Morita rings with zero bimodule homomorphisms is given by the theory of recollements.

Key words: Gorenstein FP-injective module, Morita ring, Gorenstein injective module

CLC Number: 

  • O153.3
1 AUSLANDER M , BRIDGER M . Stable module theory[M]. Providence Rbode Island: American Mathematical Society, 1969.
2 ENOCHS E E , JENDA O M G . Gorenstein injective and projective modules[J]. Mathematische Zeitschrift, 1995, 220 (1): 611- 633.
doi: 10.1007/BF02572634
3 HOLM H . Gorenstein homological dimensions[J]. Journal of Pure and Applied Algebra, 2004, 189 (1/2/3): 167- 193.
4 MAO Lixin , DING Nanqing . Gorenstein FP-injective and Gorenstein flat modules[J]. Journal of Algebra and Its Applications, 2008, 7 (4): 491- 506.
5 GAO N , PSAROUDAKIS C . Gorenstein homological aspects of monomorphism categories via Morita rings[J]. Algebras and Representation Theory, 2017, 20 (2): 487- 529.
doi: 10.1007/s10468-016-9652-1
6 YAN Meiqi , YAO Hailou . Pure projective modules and FP-injective modules over Morita rings[J]. Frontiers of Mathematics in China, 2020, 15 (6): 1265- 1293.
doi: 10.1007/s11464-020-0877-2
7 吴德军, 周慧. 三角矩阵环上Gorenstein FP-内射模的刻画[J]. 山东大学学报(理学版), 2021, 56 (8): 86- 93.
doi: 10.6040/j.issn.1671-9352.0.2021.062
WU Dejun , ZHOU Hui . A characterization of Gorenstein FP-injective modules over triangular matrix rings[J]. Journal of Shandong University(Natural Science), 2021, 56 (8): 86- 93.
doi: 10.6040/j.issn.1671-9352.0.2021.062
8 GREEN E L . On the representation theory of rings in matrix form[J]. Pacific Journal of Mathematics, 1982, 100 (1): 123- 138.
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