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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).

Information

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

REFERENCES

1.Beidleman, J. C., On Near-rings and Near-ring Modules (Doctoral Dissertation, Penn. State Univ., 1964).Google Scholar
2.Betsch, G., Primitive near-rings, Math. Z. 130 (1973), 351–361.CrossRefGoogle Scholar
3.Dancs-Grove, S., Locally finite near-fields, Abh. Math. Sent. Univ. Hamburg 48 (1979), 89–107.Google Scholar
4.Herstein, I., Noncommutative Rings (Carus Monograph 15 MAA, John Wiley and Sons, N.Y., 1965).Google Scholar
5.Maxson, C., Pettet, M. and Smith, K., On semisimple rings that are centralizer near-rings, Pacific J. Math. (to appear).Google Scholar
6.Maxsonc, C. and Smith, K., The centralizer of a group automorphism, J. Alg. 54 (1978), 27–34.Google Scholar
7.Maxson, C. and Smith, K., The centralizer of a set of group automorphisms, Comm. in Alg. 8 (1980), 211–230.CrossRefGoogle Scholar
8.Maxson, C. and Smith, K., Centralizer near-rings that are endomorphism rings, Proc. Amer. Math. Soc. 80 (1980), 189–195.CrossRefGoogle Scholar
9.Meldrum, J. and Oswald, A., Near-rings of mappings, Proc. Royal Soc. Edinburgh 83A (1978), 213–223.Google Scholar
10.Passman, D., Permutation Groups (W. A. Benjamin, N.Y., 1968).Google Scholar
11.Pilz, G., Near-rings (North-Holland, New York, 1977).Google Scholar
12.Ramakotaiah, D., Isomorphisms of near-rings of transformations, J. London Math. Soc. (2) 9 (1974), 272–278.CrossRefGoogle Scholar
13.Wielandt, H., Über Bereiche aus Gruppenabbildungen, Deutsche Mathematik 3 (1938), 9–10.Google Scholar