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Pseudo-distributive near-rings

Published online by Cambridge University Press:  17 April 2009

Henry E. Heatherly  and
Steve Ligh
Henry E. Heatherly
Affiliation:
Department of Mathematics, College of Liberal Arts, University of Southwestern Louisiana, Lafayette, Louisiana, USA.
Steve Ligh
Affiliation:
Department of Mathematics, College of Liberal Arts, University of Southwestern Louisiana, Lafayette, Louisiana, USA.
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Abstract

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In the study of the theory of rings, matrix rings, group rings, algebras, and so on, play a very important role. However, the analogous systems may not exist in the theory of near-rings. Recently Ligh obtained a necessary and sufficient condition for the set of n × n matrices with entries from a near-ring to be a near-ring. This opens the door for the study of other structures such as group near-rings, algebras, and so on. In this paper we initiate a study of the basic properties of pseudo-distributive near-rings, which is exactly the class of near-rings needed to carry out the construction of matrix near-rings, group near-rings, polynomials with near-ring coefficients, and so on.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 3 , June 1975 , pp. 449 - 456
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Beidleman, James C., “On near-rings and near-ring modules”, (Doctoral Dissertation, Pennsylvania State University, 1964).Google Scholar
[2]Bell, Howard and Ligh, Steve “On finiteness conditions for near rings”, Publ. Math. Debrecen (to appear).Google Scholar
[3]Clay, James R., “The near-rings on groups of low order”, Math. Z. 104 (1968), 364–371.Google Scholar
[4]Heatherly, Henry Edward, “Embedding of near-rings”, (Doctoral Dissertation, Texas A&M University, 1968).Google Scholar
[5]Laffey, Thomas J., “Infinite rings with all proper subrings finite”, Amer. Math. Monthly 81 (1974), 270–272.CrossRefGoogle Scholar
[6]Ligh, Steve, “A note on matrix near rings”, J. London Math. Soc. (to appear).Google Scholar