Geodesic
Spectral Sequence and Finitely Presented Dimension for Weak Hopf--Galois Extensions
Matematičeskie zametki, Tome 98 (2015) no. 5, pp. 756-768

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Let $H$ be a weak Hopf algebra, $A$ a right weak $H$-comodule algebra, and $B$ the subalgebra of the $H$-coinvariant elements of $A$. Let $A/B$ be a right weak $H$-Galois extension. In this paper, a spectral sequence for $\operatorname{Ext}$ which yields an estimate for the global dimension of $A$ in terms of the corresponding data for $H$ and $B$ is constructed. Next, the relationship between the finitely presented dimensions of $A$ and its subalgebra $B$ are given. Further, the case in which $A$ is an $n$-Gorenstein algebra is studied.
Keywords: weak Hopf–Galois extension, spectral sequence, finitely presented dimension, Gorenstein algebra. 
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     author = {X. Y. Zhou and T. Yang},
     title = {Spectral {Sequence} and {Finitely} {Presented} {Dimension} for {Weak} {Hopf--Galois} {Extensions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {756--768},
     publisher = {mathdoc},
     volume = {98},
     number = {5},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_98_5_a8/}
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X. Y. Zhou; T. Yang. Spectral Sequence and Finitely Presented Dimension for Weak Hopf--Galois Extensions. Matematičeskie zametki, Tome 98 (2015) no. 5, pp. 756-768. http://geodesic.mathdoc.fr/item/MZM_2015_98_5_a8/