Is an irng singly generated as an ideal?
Rings and Algebras
2013-07-12 v2 Group Theory
Abstract
Recall that a rng is a ring which is possibly non-unital. In this note, we address the problem whether every finitely generated idempotent rng (abbreviated as irng) is singly generated as an ideal. It is well-known that it is the case for a commutative irng. We prove here it is also the case for a free rng on finitely many idempotents and for a finite irng. A relation to the Wiegold problem for perfect groups is discussed.
Keywords
Cite
@article{arxiv.1112.1802,
title = {Is an irng singly generated as an ideal?},
author = {Nicolas Monod and Narutaka Ozawa and Andreas Thom},
journal= {arXiv preprint arXiv:1112.1802},
year = {2013}
}
Comments
5 pages, no figures