Author:
LEROY ANDRÉ,MATCZUK JERZY
Abstract
AbstractThe 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 σ of a prime one-sided noetherian ringRis injective whenever the image σ(R) contains an essential left idealLofR. If, in addition, σ(L)=L, then σ is an automorphism ofR. Examples showing that the assumptions imposed onRcannot be weakened toRbeing a prime left Goldie ring are provided. Two open questions are formulated.
Publisher
Cambridge University Press (CUP)