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Let $R\subset S$ be a Frobenius extension of rings and $M$ a left $S$-module and let $\mathcal{X}$ be a class of left $R$-modules and $\mathcal{Y}$ a class of left $S$-modules. Under some conditions it is proven that $M$ is a $\mathcal{Y}$-Gorenstein left $S$-module if and only if $M$ is an $\mathcal{X}$-Gorenstein left $R$-module if and only if $\tp{S}{M}$ and $\Hom{S}{M}$ are $\mathcal{Y}$-Gorenstein left $S$-modules. This statement extends a known corresponding result. In addition, the situations of Ding modules, Gorenstein AC modules and projectively coresolved Gorenstein flat modules are considered under Frobenius extensions.
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참고문헌 (25)
참고문헌 신청
M. Auslander / 1969 / Stable module theory / American Mathematical Society
M. Auslander / 1956 / HOMOLOGICAL DIMENSION IN NOETHERIAN RINGS / Proceedings of the National Academy of Sciences 42(1):36~38
D. Bravo / 2014 / The stable module category of a general ring / arXiv:1405.5768
NANQING DING / 2009 / STRONGLY GORENSTEIN FLAT MODULES / Journal of the Australian Mathematical Society 86(3):323~338
Edgar E. Enochs / 1995 / Gorenstein injective and projective modules / Mathematische Zeitschrift 220(1):611~633
M. Auslander / 1956 / HOMOLOGICAL DIMENSION IN NOETHERIAN RINGS / Proceedings of the National Academy of Sciences 42(1):36~38
D. Bravo / 2014 / The stable module category of a general ring / arXiv:1405.5768
NANQING DING / 2009 / STRONGLY GORENSTEIN FLAT MODULES / Journal of the Australian Mathematical Society 86(3):323~338
Edgar E. Enochs / 1995 / Gorenstein injective and projective modules / Mathematische Zeitschrift 220(1):611~633
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