2013/10/18 by Lars Kadison, Kadison, Lars
Mathematics · #12F10 #13B02 #16D20 #16H05 #16S34 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:12F10 #msc:13B02 #msc:16D20 #msc:16H05 #msc:16S34
paper · pdf · doi:10.48550/arxiv.1310.4987
19 pages. Added a module condition characterizing H-separable extension, a Frobenius extension condition so that left and right tower conditions are equivalent, and a going up and down proposition between the tower conditions here and in http://arxiv.org/abs/0707.3756
arxiv created 2014/01/27 · arxiv updated 2014/01/28
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 two 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.