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Near-rings associated with generalized translation structures
Authors:Carlton J. Maxson
Affiliation:(1) Mathematics Department, Texas A&M University, 77843 College Station, TX, USA
Abstract:In this paper we study generalized translation spaces with operators, denoted by GTSO. We associate to each GTSO a near-ring, called the kernel of the GTSO. Focusing on the finite case we show that every near-ring with identity arises as the kernel of an appropriate GTSO. In terms of the geometric properties of the GTSO we obtain representation results for the classes of local near-rings and near-fields.
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