Left Self-Distributive Rings and Nearrings

  • Gary F. Birkenmeier

Abstract

A (near-) ring R is called left self-distributive, LSD, if vxy = vxvy for all v,x,y in R. Right self-distributive (near-) rings, RSD, are defined similarly. A (near-) ring is called self-distributive, SD, if it is both LSD and RSD. Observe that the class of LSD (left near-) rings is exactly the class of (left near-) rings for which each left multiplication mapping (i.e., xax) is a (left near-) ring endomorphism. Hence the class of LSD (left near-)rings includes the AE-(left near-) rings (i.e., those (left near-) rings for which every additive endomorphism is a (left near-) ring endomorphism). In this paper we will discuss the history and recent developments for the class of LSD and related (left near-) rings. Examples will be included to illustrate and delimit the theory.

Keywords

Clay Malone 

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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Gary F. Birkenmeier
    • 1
  1. 1.Department of MathematicsUniversity of Southwestern LouisianaLafayetteUSA

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