JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (3): 33-38.doi: 10.6040/j.issn.1671-9352.0.2022.285

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Strongly V W -Gorenstein complexes

JIA Hong-hui, ZHAO Ren-yu   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2023-03-02

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Abstract: Let V, W be two classes of R-modules. A notion of strongly V W -Gorenstein complexes is introduced. It is shown that if V, W are closed under extensions and finite direct sums, V ⊥V, W ⊥W, V ⊥W and V,W ⊆G(V W ), a complex M is strongly V W -Gorenstein if and only if M is exact and Zn(M)is V W -Gorenstein for all n∈Z. In addition, some interesting corollaries are obtained, which unify and genelize some known results.

Key words: V W -Gorenstein module, strongly V W -Gorenstein complex, W -complex, CE W -complex

CLC Number: 

  • O153.3
[1] ENOCHEE, JENDA O M G. Gorenstein injective and projective modules[J]. Mathematische Zeitschrift, 1995, 220(4):611-633.
[2] HOLM H. Gorenstein homological dimensions[J]. Journal of Pure and Applied Algebra, 2004, 189(1/2/3):167-193.
[3] GENG Yuxian, DING Nanqing. W -Gorenstein modules[J]. Journal of Algebra, 2011, 325:132-146.
[4] SATHER-WAGSTAFF S, SHARIF T, WHITE D. Stability of Gorenstein categories [J]. Journal of the London Mathematical Society-Second: Series, 2008, 77(2):481-502.
[5] HOLM H, JØRGENSEEN P. Semi-dualizing modules and related Gorenstein homological dimensions[J]. Journal of Pure and Applied Algebra, 2006, 205(2):423-445.
[6] WHITE D. Gorenstein projective dimension with respect to a semidualizing module[J]. Journal of Commutative Algebra, 2010, 2(1):111-137.
[7] ZHAO Guoqiang, SUN Juxiang. V W -Gorenstein categories[J]. Turkish Journal of Mathematics, 2016, 40(2):365-375.
[8] ZHAO Renyu, REN Wei. V W -Gorenstein complexes[J]. Turkish Journal of Mathematics, 2017, 41:537-547.
[9] ENOCHS E E, GARCA ROZAS J R. Gorenstein injective and projective complexes[J]. Communications in Algebra, 1998, 26(5):1657-1674.
[10] YANG Xiaoyan, LIU Zhongkui. Gorenstein projective, injective and flat complexes[J]. Communications in Algebra, 2011, 39:1705-1721.
[11] LIANG Li, DING Nanqing, YANG Gang. Some remarks on projective generators and injective cogenerators[J]. Acta Mathematical Sinica: English Seriesa, 2014, 30:2063-2078.
[12] YANG Chunhua, LIANG Li. Gorenstein injective and projective complexes with respect to a semidualizing module[J]. Communications in Algebra, 2012, 40:3352-3364.
[13] LU Bo, LIU Zhongkui. A note on Gorenstein projective complexes[J]. Turkish Journal of Mathematics, 2016, 40:235-243.
[14] LU Bo. Strongly W -Gorenstein complexes[J]. Journal of Mathematical Research with Applications, 2018, 38(5):449-457.
[15] GILLESPIE J. The flat model structure on Ch(R)[J]. Transactions of the American Mathematical Society, 2004, 356:3369-3390.
[16] ENOCHS E E. Cartan-Eilenberg complexes and resolutions[J]. Journal of Algebra, 2011, 342:16-39.
[17] HOLM H, WHITE D. Foxby equivalence over associative rings[J]. Journal of Mathematics of Kyoto University, 2007, 47(4):781-808.
[18] LU Bo, LIU Zhongkui. A note on Cartan-Eilenberg Gorenstein categories[J]. Kodai Mathematical Journal, 2015, 102(1):209-227.
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