2024/05/06 by mohamed hamam, Hamam, M. M., R. E. Abdel-Khalek +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2405.03423
openalex publication_date 2024/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R be a ring with identity, (S,≤) an ordered monoid, ω:S → End(R) a monoid homomorphism, and A= R[[S,ω]] the ring of skew generalized power series. The concepts of generalized Baer and generalized quasi-Baer rings are generalization of Baer and quasi-Baer rings, respectively. A ring R is called generalized right Baer (generalized right quasi-Baer) if for any non-empty subset S (right ideal I) of R, the right annihilator of Sn \space0.1cm(In) is generated by an idempotent for some positive integer n. Left cases may be defined analogously. A ring R is called generalized Baer (generalized quasi-Baer) if it is both generalized right and left Baer (generalized right and left quasi-Baer) ring. In this paper, we examine the behavior of a skew generalized power series ring over a generalized right Baer (generalized right quasi-Baer) ring and prove that, under specific conditions, the ring A is generalized right Baer (generalized right quasi-Baer) if and only if R is a generalized right Baer (generalized right quasi-Baer) ring.