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Almost Multiplication Rings

Published online by Cambridge University Press:  20 November 2018

H. S. Butts  and
R. C. Phillips
H. S. Butts
Affiliation:
Louisiana State University
R. C. Phillips
Affiliation:
Wofford College
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It is well known that an ideal A in a. Dedekind domain has a prime radical if and only if A is a power of a prime ideal. The purpose of this paper is to determine necessary and sufficient conditions in order that a commutative ring with unit element have this property and to study the ideal theory in such rings. Domains with unit element having the above property possess many of the characteristics of Dedekind domains (however, they need not be Noetherian) and will be referred to in this paper as "almost Dedekind domains"—these domains are considered in Section 1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 267 - 277
Copyright
Copyright © Canadian Mathematical Society 1965

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