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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on modules over a commutative regular ring


Author: Mark L. Teply
Journal: Proc. Amer. Math. Soc. 29 (1971), 267-268
MSC: Primary 13.40
MathSciNet review: 0276214
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Abstract: An example is given of a commutative, von Neumann regular ring R, which has a module A satisfying the following conditions: (1) $ T(A) = \{ a \in A\vert(0:a)$ is an essential ideal of R} is a cyclic R-module; (2) $ A/T(A)$ is a cyclic R-module; and (3) $ T(A)$ is not a direct summand of A. This answers in the negative a question raised by R. S. Pierce.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0276214-2
PII: S 0002-9939(1971)0276214-2
Keywords: Regular ring, torsion submodule, Boolean ring, direct summand, cyclic module
Article copyright: © Copyright 1971 American Mathematical Society