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Characterizations of *-Multiplication Domains

Published online by Cambridge University Press:  20 November 2018

Evan G. Houston ,
Saroj B. Malik  and
Joe L. Mott
Evan G. Houston
Affiliation:
Dept. of Mathematics U. of NC at Charlotte Charlotte NC 28223
Saroj B. Malik
Affiliation:
D/80 Malviyanagar New Delhi (110017)India
Joe L. Mott
Affiliation:
Dept. of Mathematics Florida St. Univ. Tallahassee, FL 32306
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Abstract

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Let * be a finite-type star-operation on an integral domain D. If D is integrally closed, then D is a *-multiplication domain (the *-finite *-ideals form a group) if and only if each upper to 0 in D[x] contains an element f with c(f)* = D. A finite-type star operation on D[x] naturally induces a finite-type star operation on D, and, if each *-prime ideal P of D[x] satisfies P ∩ D = 0 or P = (P ∩ D)D[x], then D[x] is a *-multiplication domain if and only if D is.

Keywords

13F0513F2013G05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 1 , 01 March 1984 , pp. 48 - 52
Copyright
Copyright © Canadian Mathematical Society 1984

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