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Proceedings of the American Mathematical Society

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

 
 

 

Localizing prime idempotent kernel functors


Author: S. K. Sim
Journal: Proc. Amer. Math. Soc. 47 (1975), 335-337
MSC: Primary 16A62
DOI: https://doi.org/10.1090/S0002-9939-1975-0369436-7
MathSciNet review: 0369436
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Abstract: In this note, we call a prime idempotent kernel functor a localizing prime if it has the so-called property (T) of Goldman. We generalize a theorem of Heinicke to characterize localizing prime idempotent kernel functors and present an example of a prime idempotent kernel functor on $ \operatorname{Mod-}R$, the category of unitary right $ R$-modules, which is not a localizing prime, even though $ R$ is a right artinian ring.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0369436-7
Keywords: Idempotent kernel functor, prime idempotent kernel functor, property (T), localizing prime idempotent kernel functor, module of quotients, ring of quotients, supporting module, irreducible module, right artinian ring, right noetherian ring, socle
Article copyright: © Copyright 1975 American Mathematical Society

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