Is an irng singly generated as an ideal?

Details Is an irng singly generated as an ideal? Is an irng singly generated as an ideal?

2011-12-08

arxiv.org/abs/1112.1802v2

Mathematics

Rings and Algebras

5 pages, no figures

Scientific paper

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.

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