Journal Name:
- European Journal of Pure and Applied Mathematics
| Author Name | University of Author |
|---|---|
Abstract (2. Language):
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 Prüfer ⋆-multiplication domain if and only
if (a) ∩ (b) is ⋆f -invertible for all a, b ∈ 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 Prüfer ⋆-multiplication domain, then (a) ∩ (b) is ⋆f -invertible for all a, b ∈ R \ {0}. The converse
holds only if ⋆f = t.
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