2022/01/20 by Héctor Suárez, Suárez, Héctor, Armando Reyes +1
Mathematics · #16S36 #16T20 #16W20 #16W80 #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2201.08339
openalex publication_date 2022/01/20 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
In this paper, we introduce the concept of Σ-semicommutative ring, for Σ a finite family of endomorphisms of a ring R. We relate this class of rings with other classes of rings such that Abelian, reduced, Σ-rigid, nil-reversible and rings satisfying the Σ-skew reflexive nilpotent property. Also, we study some ring-theoretical properties of skew PBW extensions over Σ-semicommutative rings. We prove that if a ring R is Σ-semicommutative with certain conditions of compatibility on derivations, then for every skew PBW extension A over R, R is Baer if and only if R is quasi-Baer, and equivalently, A is quasi-Baer if and only if A is Baer. Finally, we consider some topological conditions for skew PBW extensions over Σ-semicommutative rings.