Is an irng singly generated as an ideal?

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.


Published in:
International Journal of Algebra and Computation, 22, 4
Year:
2012
Publisher:
World Scientific Publishing
ISSN:
0218-1967
Laboratories:




 Record created 2011-12-11, last modified 2018-03-17

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