We introduce the notion of an 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, D B 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 a bijective antipode. © 2007 Elsevier Ltd. All rights reserved.
Publication Source (Journal or Book title)
Journal of Pure and Applied Algebra
Chen, Y., Ng, S., & Shum, K. (2008). On radicals of module coalgebras. Journal of Pure and Applied Algebra, 212 (1), 157-167. https://doi.org/10.1016/j.jpaa.2007.05.009