A tower condition characterizing normality

Lars KADISON

doi:10.14492/hokmj/1470139403

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Home > Journals > Hokkaido Math. J. > Volume 45 > Issue 2 > Article

June 2016 A tower condition characterizing normality

Lars KADISON

Hokkaido Math. J. 45(2): 243-262 (June 2016). DOI: 10.14492/hokmj/1470139403

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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.