Star operations on modules (Q1028293)

The authors generalize the theory of (semi)star operations (defined on integral domains) to the case of torsion free modules over integral domains. After listing basic properties, the authors prove that unlike integral domains, semistar operations of finite type on modules do not necessarily induce s localizing system of finite type. Further, they give necessary and sufficient conditions for a semistar operation on a module to be stable. Namely, they prove that for a torsion free \(D\)-module \(M\) and for a a \(D\)-semistar operation \(*\) on \(M\), \(*\) is stable if and only if \(*=*_{\mathcal{F}^{*}}\). The paper closes with a section on star cancellation problem.