Geodesic
On Rings with Many Endomorphisms
Canadian mathematical bulletin, Tome 19 (1976) no. 2, pp. 199-204

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DOI

All rings have an identity, all homomorphisms map identities to identities, all homomorphisms on algebras over fields are algebra homomorphisms. A ring R is a quotient-embeddable ring (a QE-ring) if for any proper ideal a of R there is an endomorphism of R whose kernel is the ideal a. A QE-ring U is a receptor of R if for any proper ideal a of R there is a homomorphism from R to U whose kernel is the ideal a.Theorem. A ring R has a receptor if and only if it is a K-algebra over some field K contained in the center of R. If R is a commutative K-algebra of this type, then it has a commutative receptor.
DOI : 10.4153/CMB-1976-030-3
Mots-clés : 16A06, 13B20, 13B25, Free associative algebras, polynomial rings, algebras, homomorphism, quotient-embeddable rings, receptors 
Neggers, Joseph. On Rings with Many Endomorphisms. Canadian mathematical bulletin, Tome 19 (1976) no. 2, pp. 199-204. doi: 10.4153/CMB-1976-030-3
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     title = {On {Rings} with {Many} {Endomorphisms}},
     journal = {Canadian mathematical bulletin},
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     year = {1976},
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     number = {2},
     doi = {10.4153/CMB-1976-030-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-030-3/}
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