Semiprimeness, quasi-Baerness and prime radical of skew generalized power series rings. Issue 6 (3rd June 2017)

• Record Type: Journal Article
• Authors: Paykan, Kamal; Moussavi, Ahmad
• Is Part Of: Communications in algebra. Volume 45:Issue 6(2017)
• Page Start: 2306
• Page End: 2324
• Publication Date: 2017-06-03
• Subjects: Prime radical -- Quasi-Baer ring -- (S, ω)-Baer ring -- (S, ω)-prime -- (S, ω)-quasi Baer ring -- (S, ω)-semiprime -- skew generalized power series ring; 16S99 -- 16W60 -- Secondary: 06F05 -- 16P60 -- 16S36 -- 16U80 -- 20M25; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1233198
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: Let R be a ring, ( S, ≤) a strictly ordered monoid and ω : S → End ( R ) a monoid homomorphism. The skew generalized power series ring R [[ S, ω ]] is a common generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomial rings, (skew) group rings, and Mal'cev-Neumann Laurent series rings. In this paper we obtain necessary and sufficient conditions for the skew generalized power series ring R [[ S, ω ]] to be a semiprime, prime, quasi-Baer, or Baer ring. Furthermore, we study the prime radical of a skew generalized power series ring R [[ S, ω ]]. Our results extend and unify many existing results. In particular, we obtain new theorems on (skew) group rings, Mal'cev-Neumann Laurent series rings and the ring of generalized power series.