On GI-flat modules and dimensions
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Let R be a ring. A right R-module M is called GI-flat ifTorR1 (M,G) = 0 for every Gorenstein injective left R-module G. It isshown that GI-flat modules lie strictly between flat modules and copureflat modules. Suppose R is an n-FC ring, we prove that a finitely pre-sented right R-module M is GI-flat if and only if M is a cokernel of aGorenstein flat preenvelope K→F of a right R-module K with F flat. Then we study GI-flat dimensions of modules and rings. Various resultsin [6] are developed, some new characterizations of von Neumann regularrings are given.
Abstract
Let R be a ring. A right R-module M is called GI-flat ifTorR1 (M,G) = 0 for every Gorenstein injective left R-module G. It isshown that GI-flat modules lie strictly between flat modules and copureflat modules. Suppose R is an n-FC ring, we prove that a finitely pre-sented right R-module M is GI-flat if and only if M is a cokernel of aGorenstein flat preenvelope K→F of a right R-module K with F flat. Then we study GI-flat dimensions of modules and rings. Various resultsin [6] are developed, some new characterizations of von Neumann regularrings are given.
참고문헌 (22)
- D. Bennis, "A note on Gorenstein flat dimension", Algebra Colloq, 18(1), pp.155~161 (2011)
- D. Bennis, "Strongly Gorenstein projective, injective, and flat modules", J. Pure Appl. Algebra, 210(2), pp.437~445 (2007)
- H. Cartan, "Homological Algebra" (1956), Princeton University Press
- L. W. Christensen, "Gorenstein Dimensions", pp.1747~ (2000), Springer– Verlag
- R. R. Colby, "Rings which have flat injective modules", J. Algebra, 35, pp.239~252 (1975)
- N. Q. Ding, "The flat dimensions of injective modules", Manuscripta Math, 78(2), pp.165~177 (1993)
- N. Q. Ding, "On copure flat modules and flat resolvents", Comm. Algebra, 24(3), pp.1071~1081 (1996)
- N. Q. Ding, "Coherent rings with finite self-FP-injective dimension", Comm. Algebra, 24(9), pp.2963~2980 (1996)
- E. E. Enochs, "Copure injective resolutions, flat resolvents and dimensions", Comment. Math. Univ. Carolin, 34(2), pp.203~211 (1993)
- E. E. Enochs, "Gorenstein injective and projective modules", Math. Z, 220(4), pp.611~633 (1995)
- E. E. Enochs, "Relative Homological Algebra" (2000), Walter de Gruyter
- E. E. Enochs, "The existence of Gorenstein flat covers", Math. Scand, 94(1), pp.46~62 (2004)
- E. E. Enochs, "Gorenstein flat modules", Nanjing Daxue Xuebao Shuxue Bannian Kan, 10(1), pp.1~9 (1993)
- C. Faith, "Algebra I: Rings, Modules and Categories" (1981), Springer
- D. J. Fieldhouse, "Character modules, dimension and purity", GlasgowMath. J, 13, pp.144~146 (1972)
- Z. H. Gao, "On GI-injective modules", Comm. Algebra, 40(10), pp.3841~3858 (2012)
- H. Holm, "Gorenstein homological dimensions", J. Pure Appl. Algebra, 189(1-3), pp.167~193 (2004)
- L. X. Mao, "Gorenstein FP-injective and Gorenstein flat modules", J. Algebra Appl, 7(4), pp.491~506 (2008)
- J. J. Rotman, "An Introduction to Homological Algebra" (1979), Academic Press
- R. Sazeedeh, "Strongly torsion free, copure flat and Matlis reflexive modules", J. Pure Appl. Algebra, 192(1-3), pp.265~274 (2004)
- J. Z. Xu, "Flat Covers of Modules", pp.1996~, Springer-Verlag
- X. Y. Yang, "Strongly Gorenstein projective, injective and flat modules", J. Algebra, 320(7), pp.2659~2674 (2008)