Geodesic
RING ENDOMORPHISMS WITH LARGE IMAGES
Glasgow mathematical journal, Tome 55 (2013) no. 2, pp. 381-390

Voir la notice de l'article provenant de la source Cambridge University Press

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 σ of a prime one-sided noetherian ring R is injective whenever the image σ(R) contains an essential left ideal L of R. If, in addition, σ(L)=L, then σ is an automorphism of R. Examples showing that the assumptions imposed on R cannot be weakened to R being a prime left Goldie ring are provided. Two open questions are formulated.
DOI : 10.1017/S0017089512000626
Mots-clés : 16W20, 16P60 
LEROY, ANDRÉ; MATCZUK, JERZY. RING ENDOMORPHISMS WITH LARGE IMAGES. Glasgow mathematical journal, Tome 55 (2013) no. 2, pp. 381-390. doi: 10.1017/S0017089512000626
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