Turkish Journal of Mathematics
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 $\mbox{r.cot.D}(A)\leq\mbox{r.cot.D}(B)+\mbox{l.D}(H)$. Moreover, we give some sufficient conditions for which $\mbox{r.cot.D}(A)=\mbox{r.cot.D}(B)$. As applications, we obtain some results about cotorsion dimension of the smash product.
DOI
10.3906/mat-1408-59
Keywords
Hopf--Galois extension, cotorsion dimension, smash product
First Page
108
Last Page
113
Recommended Citation
ZHOU, X, & WEI, M (2016). Notes on cotorsion dimension of Hopf--Galois extensions. Turkish Journal of Mathematics 40 (1): 108-113. https://doi.org/10.3906/mat-1408-59
