Similarity, Codepth Two Bicomodules and QF Bimodules

Details Similarity, Codepth Two Bicomodules and QF Bimodules Similarity, Codepth Two Bicomodules and QF Bimodules

2007-12-28

arxiv.org/abs/0712.4362v2

Mathematics

Rings and Algebras

11 pages

Scientific paper

For any k-coalgebra C it is shown that similar quasi-finite C-comodules have strongly equivalent coendomorphism coalgebras; (the converse is in general not true). As an application we give a general result about codepth two coalgebra homomorphisms. Also a notion of codepth two bicomodule is introduced. The last section applies similarity to an endomorphism ring theorem for quasi-Frobenius (QF) bimodules and then to finite depth ring extensions. For QF extensions, we establish that left and right depth two are equivalent notions as well as a converse endomorphism theorem, and characterize depth three in terms of separability and depth two.

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