A fresh look into skew inverse Laurent series rings. Issue 4 (2nd April 2020) - Hashemi, Ebrahim; Hamidizadeh, Maryam; Alhevaz, Abdollah
Abstract: Skew inverse Laurent series rings have been actively investigated recently, and many interesting results have been obtained in the literature. In this paper, by a fresh look, we obtain further results on skew inverse Laurent series rings. First, we give some radical-theoretic properties of this ring construction, giving a characterization of the Jacobson radical of the skew inverse Laurent series ring R ( ( x − 1 ; α, δ ) ), where the base coefficient ring R is a 2-primal ring and every minimal prime ideal of R is ( α, δ ) -ideal. As a consequence of the results in first part, we will be able to add a new class of rings, to the several special classes of rings previously shown satisfying the famous Köthe's Conjecture. We also characterize when a skew inverse Laurent series ring R ( ( x − 1 ; α, δ ) ) is clean, and we obtain partial characterizations for it to be semiperfect or semiregular.