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.
2000 ◽
Vol 42
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pp. 97-113
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2000 ◽
Vol 10
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pp. 719-745
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2019 ◽
Vol 19
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pp. 2050050
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1976 ◽
Vol 21
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pp. 299-309
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