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On the Cardinality of Subrings of a Commutative Ring

Published online by Cambridge University Press:  20 November 2018

Robert Gilmer  and
William Heinzer
Robert Gilmer
Affiliation:
Department of Mathematics, Florida State UniversityTallahassee, Florida 32306, U.S.A.
William Heinzer
Affiliation:
Department of Mathematics, Purdue UniversityW. Lafayette, Indiana 47907, U.S.A.
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Abstract

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If R is an uncountable commutative ring, it is shown that there exists a proper subring of R having the same cardinality as R. It is also shown that if |R| = ω is an uncountable regular cardinal, and if R1 is a subring of R containing an identity of R and such that |R1| < ω, then there exists a proper R1-subalgebra S of R such that |S| = |R|.

Keywords

13B0213C0513E05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 1 , 01 March 1986 , pp. 102 - 108
Copyright
Copyright © Canadian Mathematical Society 1986

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