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Automorphism groups of laminated near-rings

Published online by Cambridge University Press:  20 January 2009

K. D. Magill Jr
K. D. Magill Jr
Affiliation:
State University of New York at Buffalo
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Let N be an arbitrary near-ring. Each element a ∈ N determines in a natural way a new multiplication on the elements of N which results in a near-ring Na whose additive group coincides with that of N but whose multiplicative semigroup generally differs. Specifically, we define the product x * y of two elements in Na by x * y = x a y where a product in the original near-ring is denoted by juxtaposition. One easily checks that Na is a near-ring with addition identical to that of N. The original near-ring N will be referred to as the base near-ring, Na will be referred to as a laminated near-ring of N and a will be referred to as the laminating element or sometimes more simply as the laminator.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 23 , Issue 1 , February 1980 , pp. 97 - 102
Copyright
Copyright © Edinburgh Mathematical Society 1980

References

REFERENCES

(1) Magill, K. D. Jr., Semigroup structures for families of functions, II; continuous functions, J. Aust. Math. Soc. 7 (1967), 95–107.Google Scholar
(2) Magill, K. D. Jr., Semigroups and near-rings of continuous functions, General Topology and its Relations to Modern Analysis and Algebra, III, Proc. Third Prague Top. Symp., 1971 (Academia, Prague, 1972), 283–288.Google Scholar