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