A Characterisation of Morita Algebras in Terms of Covers
Copyright policy )A Characterisation of Morita Algebras in Terms of Covers
AbstractA pair (A, P) is called a cover of EndA(P)op if the Schur functor HomA(P,−) is fully faithful on the full subcategory of projective A-modules, for a given projective A-module P. By definition, Morita algebras are the covers of self-injective algebras and then P is a faithful projective-injective module. Conversely, we show that A is a Morita algebra and EndA(P)op is self-injective whenever (A, P) is a cover of EndA(P)op for a faithful projective-injective module P.
- University of Stuttgart Germany
16G10, 16S50, 16L60, self-injective algebras, Mathematics - Rings and Algebras, Endomorphism rings; matrix rings, 510, Rings and Algebras (math.RA), FOS: Mathematics, Morita algebras, Representation Theory (math.RT), Quasi-Frobenius rings, Mathematics - Representation Theory, Representations of associative Artinian rings, covers
16G10, 16S50, 16L60, self-injective algebras, Mathematics - Rings and Algebras, Endomorphism rings; matrix rings, 510, Rings and Algebras (math.RA), FOS: Mathematics, Morita algebras, Representation Theory (math.RT), Quasi-Frobenius rings, Mathematics - Representation Theory, Representations of associative Artinian rings, covers
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