Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Radicals of Module Coalgebras   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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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol