Notes on cotorsion dimension of Hopf--Galois extensions

Authors : Xiaoyan ZHOU, Min WEI

Pages : 108-113

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Let $H$ be a finite dimensional Hopf algebra over a field $k$ and $A/B$ be a right $H$-Galois extension. In this note the relationship of cotorsion dimensions between $A$ and $B$ will be studied. We prove that $\mbox{r.cot.D}insert ignore into journalissuearticles values(A);\leq\mbox{r.cot.D}insert ignore into journalissuearticles values(B);+\mbox{l.D}insert ignore into journalissuearticles values(H);$. Moreover, we give some sufficient conditions for which $\mbox{r.cot.D}insert ignore into journalissuearticles values(A);=\mbox{r.cot.D}insert ignore into journalissuearticles values(B);$. As applications, we obtain some results about cotorsion dimension of the smash product.
Keywords : Hopf Galois extension, cotorsion dimension, smash product