Abstract
We define left relative H-separable tower of rings and continue a study of these begun by Sugano. It is proven that a progenerator extension has right depth 2 if and only if the ring extension together with its right endomorphism ring is a left relative H-separable tower. In particular, this applies to twisted or ordinary Frobenius extensions with surjective Frobenius homomorphism. For example, normality for Hopf subalgebras of finite-dimensional Hopf algebras is also characterized in terms of this tower condition.
Citation
Lars KADISON. "A tower condition characterizing normality." Hokkaido Math. J. 45 (2) 243 - 262, June 2016. https://doi.org/10.14492/hokmj/1470139403
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