A fresh look into skew inverse Laurent series rings. Issue 4 (2nd April 2020)

• Record Type: Journal Article
• Authors: Hashemi, Ebrahim; Hamidizadeh, Maryam; Alhevaz, Abdollah
• Is Part Of: Communications in algebra. Volume 48:Issue 4(2020)
• Page Start: 1439
• Page End: 1451
• Publication Date: 2020-04-02
• Subjects: Clean rings -- Jacobson radical -- Köthe's conjecture -- 2-primal rings -- semiperfect rings -- skew inverse Laurent series rings -- upper (lower) nilradical; 16N20 -- 16N40 -- 16W60; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2019.1688824
• Languages: English
• ISSNs: 0092-7872

Abstract

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.