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Proceedings of the American Mathematical Society

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

 

 

Density relative to a torsion theory


Authors: Paul Bland and Stephen Riley
Journal: Proc. Amer. Math. Soc. 82 (1981), 527-532
MSC: Primary 16A64; Secondary 16A80
DOI: https://doi.org/10.1090/S0002-9939-1981-0614872-7
MathSciNet review: 614872
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Abstract: If $ (\Im, \mathcal{F})$ is a torsion theory on Mod $ R$, then a ring $ B$ of biendomorphisms of a $ \Im$-cocritical module is topologized. Moreover, if a certain factor module of $ R$ is quasi-projective, a ring monomorphism $ \varphi :R \to B$ is found such that $ \varphi (R)$ is topologically dense in $ B$. This is done in such a way that when $ (\Im, \mathcal{F})$ is the torsion theory in which every module is torsion free, the Jacobson density theorem is recovered.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0614872-7
Keywords: Torsion theory, $ \Im $-cocritical module, $ \Im $-critical right ideal, right $ \Im $-primitive ring, density theorem
Article copyright: © Copyright 1981 American Mathematical Society