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1 results

  • On Rings with Many Endomorphisms

  • Joseph Neggers
  • Journal:
    Canadian Mathematical Bulletin / Volume 19 / Issue 2 / 01 June 1976
    Published online by Cambridge University Press:
    20 November 2018, pp. 199-204
    Print publication:
    01 June 1976
    • Article
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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.