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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Artinian subrings of a commutative ring
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by Robert Gilmer and William Heinzer PDF
Trans. Amer. Math. Soc. 336 (1993), 295-310 Request permission

Abstract:

Given a commutative ring $R$, we investigate the structure of the set of Artinian subrings of $R$. We also consider the family of zero-dimensional subrings of $R$. Necessary and sufficient conditions are given in order that every zero-dimensional subring of a ring be Artinian. We also consider closure properties of the set of Artinian subrings of a ring with respect to intersection or finite intersection, and the condition that the set of Artinian subrings of a ring forms a directed family.
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 336 (1993), 295-310
  • MSC: Primary 13E10; Secondary 12D15, 12F99, 13A99
  • DOI: https://doi.org/10.1090/S0002-9947-1993-1102887-7
  • MathSciNet review: 1102887