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Proceedings of the American Mathematical Society

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

 
 

 

The Jacobson radical of the endomorphism ring of a projective module.


Authors: R. Ware and J. Zelmanowitz
Journal: Proc. Amer. Math. Soc. 26 (1970), 15-20
MSC: Primary 16.30
DOI: https://doi.org/10.1090/S0002-9939-1970-0262281-8
MathSciNet review: 0262281
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Abstract: In a recently published paper [3], the elements of the Jacobson radical of a ring of row-finite matrices over an arbitrary ring $ R$ are characterized as those matrices with entries in the Jacobson radical of $ R$ which have a vanishing set of column ideals. In this paper, the characterization is extended to include the endomorphism ring of an arbitrary projective module. In the process we offer a greatly simplified proof of the theorem for row-finite matrices.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0262281-8
Keywords: Projective modules, Jacobson radical, endomorphism ring, row-finite matrices, vanishing set of ideals
Article copyright: © Copyright 1970 American Mathematical Society

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