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.
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