Gorenstein homological invariant properties under Frobenius extensions

Zhao Zhibing

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arXiv · 1712.09111

Gorenstein homological invariant properties under Frobenius extensions

Zhao Zhibing

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Abstract

We prove that for a Frobenius extension, a module over the extension ring is Gorenstein projective if and only if its underlying module over the base ring is Gorenstein projective. For a separable Frobenius extension between Artin algebras, we obtain that the extension algebra is CM-finite (resp. CM-free) if and only if so is the base algebra. Furthermore, we prove that the reprensentation dimension of Artin algebras is invariant under separable Forbenius extensions.

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Zhao Zhibing. 2018-12-07. Gorenstein homological invariant properties under Frobenius extensions. https://arxiv.org/abs/1712.09111

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