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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Commutativity of endomorphism rings of ideals. II


Author: S. Alamelu
Journal: Proc. Amer. Math. Soc. 55 (1976), 271-274
MSC: Primary 13A99
MathSciNet review: 0401731
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Abstract: Let $ R$ be a commutative ring. In (1), it was proved that a ring $ R$ with noetherian total quotient ring is self-injective if and only if the endomorphism ring of every ideal is commutative. We prove here that if the ring is coherent and is its own total quotient ring, then $ R$ is self-injective if and only if $ \operatorname{Hom} (I,I) = R$ for every ideal $ I$ of $ R$.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0401731-6
Keywords: Total quotient ring, coherent ring, self-injective ring, irreducible ideal
Article copyright: © Copyright 1976 American Mathematical Society