Ring Endomorphisms with Large Images
Rings and Algebras
2012-07-17 v1
Abstract
The notion of ring endomorphisms having large images is introduced. Among others, injectivity and surjectivity of such endomorphisms are studied. It is proved, in particular, that an endomorphism S of a prime one-sided noetherian ring R is injective whenever the image S (R) contains an essential left ideal L of R. If additionally S(L) = L, then S is an automorphism of R. Examples showing that the assumptions imposed on R can not be weakened to R being a prime left Goldie ring are provided. Two open questions are formulated.
Cite
@article{arxiv.1207.3781,
title = {Ring Endomorphisms with Large Images},
author = {André Leroy and Jerzy Matczuk},
journal= {arXiv preprint arXiv:1207.3781},
year = {2012}
}
Comments
To appear in Glassgow Mthematical Journal, 12 pages