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Automorphism groups of laminated near-rings

  • K. D. Magill (a1)

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Let N be an arbitrary near-ring. Each element aN 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.

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References

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(1) Magill, K. D. Jr., Semigroup structures for families of functions, II; continuous functions, J. Aust. Math. Soc. 7 (1967), 95107.
(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), 283288.

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