Affiliation:
1. Department of Mathematics, Tafresh University, Tafresh, Iran
Abstract
In this paper, we continue to study skew inverse Laurent series ring [Formula: see text], where [Formula: see text] is a ring equipped with an automorphism [Formula: see text] and an [Formula: see text]-derivation [Formula: see text]. We directly prove that [Formula: see text] is semiprimitive reduced if and only if [Formula: see text] is [Formula: see text]-rigid. Also, as an application of our results, by imposing constraints on [Formula: see text] and [Formula: see text], we completely identify the Jacobson radical of [Formula: see text] whose set of all nilpotent elements has special conditions. Moreover, necessary and sufficient conditions are obtained for the skew inverse Laurent series ring to satisfy a certain ring property which is among being right Artinian, completely primary, right perfect, (semi)local, semiperfect, semiprimary, semiregular, semisimple and strongly regular, respectively.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Algebra and Number Theory