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Near-fields associated with invariant linear $ \kappa$-relations

Authors: Peter Fuchs and C. J. Maxson
Journal: Proc. Amer. Math. Soc. 103 (1988), 729-736
MSC: Primary 16A76; Secondary 12K05, 20E99
MathSciNet review: 947647
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Abstract: In this paper we investigate a construction method for subnearrings of $ M\left( G \right)$ proposed by H. Wielandt using subgroups of direct powers $ {G^\kappa }$ of $ G$ called invariant linear $ \kappa $-relations. If $ \kappa = 2$ we characterize, in terms of properties of these subgroups, when the associated near-rings are near-fields and prove that every near-field arising from an invariant linear $ 2$-relation must be a field.

References [Enhancements On Off] (What's this?)

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Article copyright: © Copyright 1988 American Mathematical Society

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