GC-projectivity and injectivity under Frobenius extensions
GC-projectivity and injectivity under Frobenius extensions
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Frobenius 扩展下的 GC 投射性和注入性
DOI：
10.1080/00927872.2022.2082460
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发表时间：
2022
影响因子：
0.7
通讯作者：
Zhibing Zhao
中科院分区：
文献类型：
--
作者：
Zhibing Zhao
本文证明了半对偶模的Gorenstein投射性和内射性在Frobenius扩张下保持不变。此外，我们还得到了模的G(C)-投射和内射维度在Frobenius扩张下是不变的。作为推论，我们得到了一些Gorenstein同调维度在Frobenius扩张下是保持的，这表明Gorenstein同调维度在Frobenius扩张下比经典的同调维度具有更好的不变性。
In this article, we prove that Gorenstein projectivity and injectivity with respect to a semidualizing module are preserved under Frobenius extensions. Furthermore, we obtain that the G(C)-projective and injective dimensions of modules are invariant under Frobenius extensions. As corollaries, we get some Gorenstein homological dimensions are preserved under Frobenius extensions, which show that Gorenstein homological dimensions have better invariant properties than the classical homological dimensions under Frobenius extensions.