Rings additively generated by periodic elements

doi:10.1142/S0219498825503220

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Rings additively generated by periodic elements

2026-02-01

PRE

Mai Hoang Bien

Peter Danchev *

M. Ramezan-Nassab

DOI：10.1142/S0219498825503220

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Abstract

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In the this 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.

Keywords:

Division rings

torsion units

periodic elements and rings