A note on Prufer *-multiplication II

Authors

  • Olivier Heubo Saginaw Valley State University

Keywords:

Star operation, ⋆-ideal, Pr¨ufer ⋆-multiplication domain

Abstract

We bring some corrections to Corollary 1 of [3]. In [3], we attempted

to show that for an arbitrary star operation ⋆ on a domain R, the domain R is

a Pr¨ufer ⋆-multiplication domain if and only if (a) \ (b) is ⋆f -invertible for all

a, b 2 R \ {0}. We show in this paper that the characterization does not hold in

general and we restate [3, Corollary 1] with justification and proof as follows: if

a domain R is a Pr¨ufer ⋆-multiplication domain, then (a)\(b) is ⋆f -invertible for

all a, b 2 R \ {0}. The converse holds only if ⋆f = t.

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Published

2016-01-27

Issue

Vol. 9 No. 1: (January 2016)

Section

Algebra

License

Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.

European Journal of Pure and Applied Mathematics will be Copyright Holder.

How to Cite

A note on Prufer *-multiplication II. (2016). European Journal of Pure and Applied Mathematics, 9(1), 1-2. https://ejpam.com/index.php/ejpam/article/view/2589