JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (12): 79-85.doi: 10.6040/j.issn.1671-9352.0.2018.713

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Gorenstein FP-projective modules and its stability

ZHANG Yu, ZHAO Ren-yu   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2019-12-11

Abstract: The concept of Gorenstein FP-projective modules is introduced as a generalization of FP-projective modules. Some properties and equivalent characterizations of Gorenstein FP-projective modules are given. The stability of the class of Gorenstein FP-projective modules is studied.

Key words: FP-projective module, Gorenstein FP-projective module, GFP-closed ring, stability

CLC Number: 

  • O153.3
[1] MAO Lixin, DING Nanqing. FP-projective dimensions[J]. Communications in Algebra, 2005, 33(4):1153-1170.
[2] HOLM H. Gorenstein homological dimensions[J]. Journal of Pure and Applied Algebra, 2004, 189(1):167-193.
[3] DING Nanqing, LI Yuanlin, MAO Lixin. Strongly Gorenstein flat modules[J]. Journal of the Australian Mathematical Society, 2009, 86(3):323-338.
[4] 朱辉辉. Gorenstein FP-投射模[J]. 山东大学学报(理学版), 2011, 46(2):110-113. ZHU Huihui. Gorenstein FP-projective modules[J]. Journal of Shandong University(Natural Science), 2011, 46(2):110-113.
[5] BENNIS D, OUARGHI K. X-Gorenstein projective modules[J]. International Mathematical Forum, 2010, 5(10):487-491.
[6] GAO Zenghui, WANG Fanggui. Coherent rings and Gorenstein FP-injective modules[J]. Communications in Algebra, 2012, 40(5):1669-1679.
[7] XU Aimin, DING Nanqing. On stability of Gorenstein categories[J]. Communications in Algebra, 2013, 41(10):3793-3804.
[8] SATHER-WAGSTAFF S, SHARIF T, WHITE D. Stability of Gorenstein categories[J]. Journal of the London Mathematical Society, 2008, 77(2):481-502.
[9] ENOCHS E E, JENDA O M G. Relative homological algebra[M]. Berlin: Walter de Gruyter, 2000.
[10] GENG Yuxian, DING Nanqing. W -Gorenstein modules[J]. Journal of Algebra, 2011, 325(1):132-146.
[11] STENSTR(¨overO)M B. Coherent rings and FP-injective modules[J]. Journal of the London Mathematical Society, 1970, 2:323-329.
[12] ROTMAN J J. An introduction to homological algebra[M]. New York: Academic Press, 1979.
[13] GILLESPIE J. On Ding injective, Ding projective, and Ding flat modules and complexes[J]. Rocky Mountain Journal of Mathematics, 2017, 47(8):2641-2673.
[14] FIELDHOUSE D J. Character modules, dimension and purity[J]. Glasgow Mathematical Journal, 1972, 13(2):144-146.
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