Frobenius扩张下的(F,A)-Gorenstein平坦模

doi:10.12677/PM.2023.136159

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Frobenius扩张下的(F,A)-Gorenstein平坦模
(F,A)-Gorenstein Flat Modules under Frobenius Extension

DOI: 10.12677/PM.2023.136159, PDF,
作者: 魏玉娟^*, 周彩霞：西北师范大学数学与统计学院，甘肃兰州
关键词: Frobenius扩张；(F；A)-Gorenstein平坦模；(F；A)-Gorenstein平坦维数；Frobenius Extensin； (F；A)-Gorenstein Flat Module； (F；A)-Gorenstein Flat Dimension

摘要: 设R⊆S是环的Frobenius扩张，M是任意左S-模，假设A是右R-模的类，B是右S-模的类，且GF_(F,B)关于扩张封闭，I(S^OP)⊆B, 在一些条件下证明了M是(F,B)-Gorenstein平坦左S-模当且仅当M是(F,A)-Gorenstein平坦左R-模当且仅当S⊗_RM是(F,B)-Gorenstein平坦左S-模。

Abstract: Let R⊆S be a Frobenius extensin of rings, M be any left S-modules. Let A be class of right R-modules and B be class of right S-modules. GF_(F,B) be closed by extension, I(S^OP)⊆B, under some conditions proved that M be (F,B)-Gorenstein flat left S-modules if and only if M be (F,A)-Gorenstein flat left S-modules if and only if S⊗_RM be (F,B)-Gorenstein flat left S-modules.

文章引用：魏玉娟, 周彩霞. Frobenius扩张下的(F,A)-Gorenstein平坦模[J]. 理论数学, 2023, 13(6): 1571-1577. https://doi.org/10.12677/PM.2023.136159

参考文献

[1]	Overtoun, M., Enochs, E. and Jendan, O. (2011) Relative Homologocal Algebra. DeGruyter, Berlin.
[2]	Holm, H. and Jorgensen, P. (2009) Cotorsion Pairs Induced by Duality Pairs. Journal of Commutative Algebra, 1, 621-633. [Google Scholar] [CrossRef]
[3]	Gillespie, J. (2019) Duality and Stable Module Categories. Journal of Pure and Applied Algebra, 223, 3425-3435. [Google Scholar] [CrossRef]
[4]	Becerril, V. (2022) -Gorenstein flat homological dimen-sions. Journal of the Korean Mathematical Society, 59, 1203-1227.
[5]	Kasch, F. (1954) Grundlagen einer Theorie der Frobeniuserweiterungen. Mathematische Annalen, 127, 453-474. [Google Scholar] [CrossRef]
[6]	Nakayama, T. and Tsuzuku, T. (1960) On Frobenius Extensions I. Na-goya Mathematical Journal, 17, 89-110. [Google Scholar] [CrossRef]
[7]	Morita, K. (1965) Adjoint Pairs of Functors and Frobenius Ex-tension. Science Reports of the Tokyo Kyoiku Daigaku, Section A, 9, 40-71.
[8]	Ren, W. (2018) Gorenstein Projective Modules and Frobenius Extensions. Science China Mathematics, 61, 1175-1186. [Google Scholar] [CrossRef]
[9]	任伟. Gorenstein平坦模与Frobenius扩张[J]. 数学学报, 2019, 62(4): 647-652.
[10]	张睿杰. Frobenius扩张环上的n-Ding投射模[D]: [硕士学位论文]. 兰州: 西北师范大学, 2020.
[11]	Holm, H. (2004) Gorenstein Homological Dimensions. Journal of Pure and Applied Algebra, 189, 167-193. [Google Scholar] [CrossRef]

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