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PDF(418 KB)
Gorenstein平坦模与Frobenius扩张
Gorenstein Flat Modules and Frobenius Extensions
设R⊂A是环的Frobenius扩张，其中A是右凝聚环，M是任意左A-模.首先证明了AM是Gorenstein平坦模当且仅当M作为左R-模也是Gorenstein平坦模.其次，证明了Nakayama和Tsuzuku关于平坦维数沿着Frobenius扩张的传递性定理的“Gorenstein版本”：若AM具有有限Gorenstein平坦维数，则GfdA（M）=GfdR（M）.此外，证明了若R⊂S是可分Frobenius扩张，则任意A-模（不一定具有有限Gorenstein平坦维数），其Gorenstein平坦维数沿着该环扩张是不变的.
Let R⊂A be a Frobenius extension of rings, where A is right coherent. Let M be any left A-module. We first show that AM is Gorenstein flat if and only if the underlying R-module RM is Gorenstein flat. Then we prove a "Gorenstein version" of Nakayama and Tsuzuku's theorem on transfer of flat dimensions along Frobenius extensions:if AM has finite Gorenstein flat dimension, then GfdA(M)=GfdR(M). Moreover, it is proved that if R ⊂ S is a separable Frobenius extension, then for any A-module (not necessarily of finite Gorenstein flat dimension), its Gorenstein flat dimension is invariant along such ring extension.
Gorenstein平坦模 / Gorenstein平坦维数 / Frobenius扩张 / 可分扩张 {{custom_keyword}} /
Gorenstein flat module / Gorenstein flat dimension / Frobenius extension / separable extension {{custom_keyword}} /
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国家自然科学基金资助项目（11871125）重庆市自然科学基金（cstc2018jcyjAX0541）及市教委科学技术研究项目（KJQN201800509）
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