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One-Dimensional Monoid Rings with n-Generated Ideals

Published online by Cambridge University Press:  20 November 2018

James S. Okon  and
J. Paul Vicknair
James S. Okon
Affiliation:
Department of Mathematics California State University San Bernardino, California 92407 U.S.A.
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Abstract

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A commutative ring R is said to have the n-generator property if each ideal of R can be generated by n elements. Rings with the n-generator property have Krull dimension at most one. In this paper we consider the problem of determining when a one-dimensional monoid ring R[S] has the n-generator property where R is an artinian ring and S is a commutative cancellative monoid. As an application, we explicitly determine when such monoid rings have the three-generator property.

Keywords

20M2513E1513F99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 3 , 01 September 1993 , pp. 344 - 350
Copyright
Copyright © Canadian Mathematical Society 1993

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