On Radicals of Module Coalgebras

Details On Radicals of Module Coalgebras On Radicals of Module Coalgebras

2006-11-22

arxiv.org/abs/math/0611660v1

J. Pure Appl. Algebra 212 (2008), no. 1, 157--167

Mathematics

Quantum Algebra

13 pages

Scientific paper

10.1016/j.jpaa.2007.05.009

We introduce the notion of idempotent radical class of module coalgebras over a bialgebra B. We prove that if R is an idempotent radical class of B-module coalgebras, then every B-module coalgebra contains a unique maximal B-submodule coalgebra in R. Moreover, a B-module coalgebra C is a member of R if, and only if, DB is in R for every simple subcoalgebra D of C. The collection of B-cocleft coalgebras, and the collection of H-projective module coalgebras over a Hopf algebra H are idempotent radical classes. As applications, we use these idempotent radical classes to give another proofs for a projectivity theorem and a normal basis theorem of Schneider without assuming bijective antipode.

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