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Transactions of the American Mathematical Society

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

 

 

Artinian subrings of a commutative ring


Authors: Robert Gilmer and William Heinzer
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
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1993-1102887-7
Keywords: Artinian subring, zero-dimensional subring, directed union of Artinian subrings, Noetherian ring, finite spectrum, hereditarily Noetherian ring, zero-dimensional pair, coefficient field, coefficient ring, absolutely algebraic field
Article copyright: © Copyright 1993 American Mathematical Society