Hostname: page-component-77c89778f8-vpsfw Total loading time: 0 Render date: 2024-07-17T01:37:34.655Z Has data issue: false hasContentIssue false

The centralizer of the general linear group

Published online by Cambridge University Press:  20 January 2009

C. J. Maxson
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843, USA
A. Oswald
Affiliation:
Department of Mathematics and Statistics, Teesside Polytechnic, BOROUGH ROAD MIDDLESBROUGH, CLEVELAND TS1 3BA, UK
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let G be a group, written additively with identity 0, but not necessarily abelian and let S be a semigroup of endomorphisms of G. The set for all is a zero-symmetric near-ring with identity under the operations of function addition and composition, called the centralizer near-ring determined by the pair (S, G). Centralizer near-rings are general, for if N is any zero-symmetric near-ring with identity then there exists a group G and a semigroup SG such that For background material and definitions relative to near-rings in general we refer the reader to the book by Pilz [7]. For material on centralizer near-rings we refer the reader to [4] and [6].

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1984

References

REFERENCES

1.Jacobson, N., Structure of Rings (Amer. Math. Soc. Coll. Publ. Vol. 37, Providence, RI, 1964).Google Scholar
2.Maxson, C. J. and Smith, K. C., The centralizer of a group automorphism, J. Algebra 54 (1978), 2741.CrossRefGoogle Scholar
3.Maxson, C. J. and Smith, K. C., Simple near-ring centralizers of finite rings, Proc. Amer. Math. Soc. 75 (1979), 812.CrossRefGoogle Scholar
4.Maxson, C. J. and Smith, K. C., The centralizer of a set of group automorphisms, Comm. in Alg. 8 (1980), 211230.CrossRefGoogle Scholar
5.Maxson, C. J. and Smith, K. C., Centralizer near-rings: Left ideals and 0-primitivity, Proc. Royal Irish Acad. 81 (1981), 187199.Google Scholar
6.Meldrum, J. D. P. and Oswald, A., Near-rings of mappings, Proc. Royal Soc. Edinburgh 83A (1978), 213223.Google Scholar
7.Pilz, G., Near-rings (North-Holland, New York, 1977).Google Scholar
8.Zeller, M., Centralizer near-rings on infinite groups (Ph.D. Dissertation, Texas A & M University, College Station, 1980).Google Scholar