A note on Prufer *-multiplication II

Olivier Heubo

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.

Keywords

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

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