### Strongly Gorenstein C-injective module and strongly Gorenstein C-flat module

ZHANG Cui-ping, LIU Ya-juan*

1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
• Online:2020-10-20 Published:2020-10-07

Abstract: Some properities of strongly Gorenstein C-injective and strongly Gorenstein C-flat modules are studied, and give the connection between the two types of modules on the specific ring.

CLC Number:

• O153.3
 [1] AUSLANDER M, BRIDGER M. Stable module theory[M]. Providence, RI: Amer Math Soc, 1969.[2] ENOCHS E E, JENDA O M G. Relative homological algebra[M]. Berlin: Walter de Gruyter, 2000.[3] BENNIS D, MAHDOU N. Strongly Gorenstein projective, injective and flat modules[J]. Journal of Pure and Applied Algebra, 2007, 210(4):437-445.[4] YANG Xiaoyan, LIU Zhongkui. Strongly Gorenstein projective, injective and flat modules[J]. Journal of Pure and Applied Algebra, 2008, 320:2659-2674.[5] HOLM H, WHITE D. Foxby equivalence over associative rings[J]. Math Kyoto Univ, 2007, 47:781-808.[6] HOLM H, JRGENSEN P. Semi-dualizing modules and related Gorenstein homological dimensions[J]. Journal of Pure and Applied Algebra, 2006, 205(2):423-445.[7] WANG Zhanping, GUO Shoutao, MA Haiyu. Stability of Gorenstein modules with respect to a semidualizing module[M]. J Math, 2017, 37(6):1143-1153.[8] ZHANG Wanru, LIU Zhongkui, YANG Xiaoyan. Foxby equivalences associated to strongly Gorenstein modules[J]. Kodai Math J, 2018, 41:397-412.[9] 李金兰,梁春丽. 强Gorenstein C -平坦模[J].山东大学学报(理学版),2017,52(12):25-31. LI Jinlan, LIANG Chunli. Strong Gorenstein C -flat modules[J]. Journal of Shangdong University(Natural Science), 2017, 52(12):25-31.[10] YANG Xiaoyan, LIU Zhongkui. C -Gorenstein projective, injective and flat modules[J]. Czechoslovak Mathematical Journal, 2010, 60(135):1109-1129.[11] XING Jianmin, XING Rufeng. Gorenstein projective, injective and flat modules relative to semidualizing modules[J]. Internation Scholarly and Scientific Research Innovation, 2014, 8(2):359-364.[12] SATHER-WAGSTAFF S, SHARIF T, WHITE D. AB-Contexts and stability for Gorenstein flat modules with respect to semidualizing modules[J]. Algebr Representation Theory, 2011, 14:403-428.[13] HOLM H. Gorenstein homological dimensions[J]. Journal of Pure and Applied Algebra, 2004,189:167-193.[14] KASCH F,WALLACE D A R. Modules and rings[M]. New York: Academic Press, 1982.[15] LAM T Y. Lectures on modules and rings[M] //Graduate Texts in Math. New York: Springer-Verlag, 1999.[16] ROTMAN JJ. An introduction to homological algebra[M]. New York: Academic Press, 1979.
 [1] LUO Xiao-qiang, TAN Ling-ling, XING Jian-min. On homological properties of C-torsionless and C-reflexive modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(4): 72-79. [2] PAN Xiao-ling, LIANG Li. Tate homology of modules of finite Gorenstein flat dimension with respect to a semidualizing module [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(12): 102-105. [3] CHEN Xiu-li, CHEN Jian-long. Homological dimensions with respect to semidualizing modules and excellent extensions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 85-89. [4] YANG Chun-hua. A note on the Gc-injective dimension of a complex [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(11): 82-86.
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