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Note on U-closed semigroup rings

Published online by Cambridge University Press:  17 April 2009

Ryûki Matsuda
Ryûki Matsuda
Affiliation:
Department of MathematicsIbaraki UniversityMito, Ibaraki 310, Japan
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Abstract

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Let D be an integral domain with quotient field K. If α2 − α ∈ D and α3 − α2 ∈ D imply α ∈ D for all elements α of K, then D is called a u-closed domain. A submonoid S of a torsion-free Abelian group is called a grading monoid. We consider the semigroup ring D[S] of a grading monoid S over a domain D. The main aim of this note is to determine conditions for D[S] to be u-closed. We shall show the following Theorem: D[S] is u-closed if and only if D is u-closed.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 3 , June 1999 , pp. 467 - 471
Copyright
Copyright © Australian Mathematical Society 1999

References

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