Artinian subrings of a commutative ring
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- by Robert Gilmer and William Heinzer
- Trans. Amer. Math. Soc. 336 (1993), 295-310
- DOI: https://doi.org/10.1090/S0002-9947-1993-1102887-7
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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.References
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Bibliographic 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