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On Rings with Many Endomorphisms

Published online by Cambridge University Press:  20 November 2018

Joseph Neggers
Joseph Neggers*
Affiliation:
Department of Mathematics, The University of Alabama, University, Alabama 35486, U.S.A.
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Abstract

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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.

Keywords

16A0613B2013B25Free associative algebraspolynomial ringsalgebrashomomorphismquotient-embeddable ringsreceptors
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 2 , 01 June 1976 , pp. 199 - 204
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Cohn, P. M., Free rings and their relations, Academic Press, New York, 1971.Google Scholar