On J-rigid rings

Abstract

Let R be a ring with an endomorphism σ. We introduce the notion of σ-J-rigid rings asa generalization of σ-rigid rings, and investigate its properties. It is proved that a ring Ris σ-J-rigid if and only if R[[x; σ]] is ¯σ-J-rigid, while the σ-J-rigid property is not Moritainvariant. Moreover, we prove that every ring isomorphism preserves J-rigid structure,and several known results are extended.