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Eleven Nonequivalent Conditions on a Commutative Ring

Published online by Cambridge University Press:  22 January 2016

Robert W. Gilmer Jr.
Robert W. Gilmer Jr.*
Affiliation:
Florida State University, Tallahassee, Florida
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We consider in this paper eleven conditions on a commutative ring R. The first of these is that R contains an identity. It is well known that each of the other properties is a consequence of the first condition. This paper considers other relations which exist between these properties. A complete diagram of all simple implications which exist between the eleven properties, together with proof of these implications, is given in section 3. Examples illustrating simple implications which do not hold are presented in section 4.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 26 , February 1966 , pp. 183 - 194
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

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