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.
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