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

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DOI

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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     title = {RING {ENDOMORPHISMS} {WITH} {LARGE} {IMAGES}},
     journal = {Glasgow mathematical journal},
     pages = {381--390},
     year = {2013},
     volume = {55},
     number = {2},
     doi = {10.1017/S0017089512000626},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000626/}
}
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