2023/11/12 by Mai Hoang Bien, Peter Danchev, Bien, M. H. +3
Computer Science · Mathematics · #16K40 #16S34 #16S50 #16U60 #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2311.06966
openalex publication_date 2023/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In the present paper, as a generalization of the classical periodic rings, we explore those rings whose elements are additively generated by two (or more) periodic elements by calling them additively periodic. We prove that, in some major cases, additively periodic rings remain periodic too; this includes, for instance, algebraic algebras, group rings, and matrix rings over commutative rings. Moreover, we also obtain some independent results for the new class of rings; for example, the triangular matrix rings retain that property.