A Note on Prufer star-multiplication Domains II

We bring some corrections to Corollary 1 of [3]. In [3], we attempted to show that for an arbitrary star operation star on a domain R, the domain R is a Prufer star-multiplication domain if and only if (a) boolean AND (b) is star(f)-invertible for all a, b is an element of 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 Prufer star-multiplication domain, then (a) boolean AND (b) is star(f)-invertible for all a, b is an element of R \ {0}. The converse holds only if star(f) = t.