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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on modules over a commutative regular ring
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by Mark L. Teply PDF
Proc. Amer. Math. Soc. 29 (1971), 267-268 Request permission

Abstract:

An example is given of a commutative, von Neumann regular ring R, which has a module A satisfying the following conditions: (1) $T(A) = \{ a \in A|(0:a)$ 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.
References
  • J. S. Alin and S. E. Dickson, Goldie’s torsion theory and its derived functor, Pacific J. Math. 24 (1968), 195–203. MR 227249
  • R. S. Pierce, Modules over commutative regular rings, Memoirs of the American Mathematical Society, No. 70, American Mathematical Society, Providence, R.I., 1967. MR 0217056
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 29 (1971), 267-268
  • MSC: Primary 13.40
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0276214-2
  • MathSciNet review: 0276214