Gorenstein homological invariant properties under Frobenius extensions

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（12）
• 页码范围: 2487-2496
• 页数: 10页
• 语种: 英文

摘要

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 (Cohen-Macaulay)-finite (resp.CM-free) if and only if so is the base algebra.Furthermore,we prove that the representation dimension of Artin algebras is invariant under separable Frobenius extensions.