Abstract
Let D be an integrally closed domain, ∗ a star-operation on D, X an indeterminate over D, and N ∗ = { f ∈ D [ X ] | ( A f ) ∗ = D } . For an e . a . b . star-operation ∗ 1 on D, let Kr ( D , ∗ 1 ) be the Kronecker function ring of D with respect to ∗ 1 . In this paper, we use ∗ to define a new e . a . b . star-operation ∗ c on D. Then we prove that D is a Prüfer ∗-multiplication domain if and only if D [ X ] N ∗ = Kr ( D , ∗ c ) , if and only if Kr ( D , ∗ c ) is a quotient ring of D [ X ] , if and only if Kr ( D , ∗ c ) is a flat D [ X ] -module, if and only if each ∗-linked overring of D is a Prüfer v-multiplication domain. This is a generalization of the following well-known fact that if D is a v-domain, then D is a Prüfer v-multiplication domain if and only if Kr ( D , v ) = D [ X ] N v , if and only if Kr ( D , v ) is a quotient ring of D [ X ] , if and only if Kr ( D , v ) is a flat D [ X ] -module.
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