Semiendomorphisms of simple near-rings

Authors:
Kirby C. Smith and Leon van Wyk

Journal:
Proc. Amer. Math. Soc. **115** (1992), 613-627

MSC:
Primary 16Y30

MathSciNet review:
1081701

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Abstract: Let be a finite simple centralizer near-ring that is not an exceptional near-field. A semiendomorphism of is a map ' from into such that , and for all . It is shown that every semiendomorphism of is an automorphism of . A Jordan-endomorphism of is a map ' from into such that , and for all . It is shown that every Jordan-endomorphism of is an automorphism assuming is invertible. The above results imply that every semiendomorphism (Jordan-endomorphism) of a "special" class of semisimple near-rings is an automorphism. These results are in contrast to the ring situation where semiendomorphisms tend to be either an automorphism or an antiautomorphism.

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DOI:
https://doi.org/10.1090/S0002-9939-1992-1081701-7

Article copyright:
© Copyright 1992
American Mathematical Society