Finiteness of the nearring of congruence preserving and 0-preserving functions of an expanded group

Peterson, Gary L. and Scott, Stuart D.: Finiteness of the nearring of congruence preserving and 0-preserving functions of an expanded group. Acta scientiarum mathematicarum, (84) 3-4. pp. 401-411. (2018)

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Abstract

In this paper we shall obtain that the nearring C0(V ) of congruence preserving functions that are 0-preserving of a tame N-module V of a nearring N is finite when N is finite. As a consequence, C0(V ) of an expanded group hV, +, Fi is finite when the nearring of 0-preserving polynomial functions P0(V ) of hV, +, Fi is finite. We then go on to obtain further consequences of this result.

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