Decompositions of Modules and Comodules
نویسنده
چکیده
It is well-known that any semiperfect A ring has a decomposition as a direct sum (product) of indecomposable subrings A = A1 ⊕ · · · ⊕ An such that the Ai-Mod are indecomposable module categories. Similarly any coalgebra C over a field can be written as a direct sum of indecomposable subcoalgebras C = ⊕ I Ci such that the categories of Ci-comodules are indecomposable. In this paper a decomposition theorem for closed subcategories of a module category is proved which implies both results mentioned above as special cases. Moreover it extends the decomposition of coalgebras over fields to coalgebras over noetherian (QF) rings.
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