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Centraliser near-ring representations

Published online by Cambridge University Press:  20 January 2009

C. J. Maxson  and
K. C. Smith
C. J. Maxson
Affiliation:
Department of Mathematics, Texas A & M University, College Station, Texas 77843, U.S.A.
K. C. Smith
Affiliation:
Department of Mathematics, Texas A & M University, College Station, Texas 77843, U.S.A.
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Let V be a group, written additively but not necessarily abelian, and let S be a semigroup of endomorphisms of V. The set C( S; V)={ f: V→ V| fσ=σ f for all σ∈ S and f(0)=0} forms a zero-symmetric near-ring with identity under the operations of function addition and composition, called the centraliser near-ring determined by S and V. Centraliser near-rings are very general, for if N is any zero-symmetric near-ring with 1 then there exists a group V and a semigroup S of endomorphisms of V such that N≃ C( S; V).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 25 , Issue 2 , June 1982 , pp. 145 - 153
Copyright
Copyright © Edinburgh Mathematical Society 1982

References

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