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 〈V, +, F〉 is finite when the nearring of 0-preserving polynomial functions P0(V) of 〈V, +, F〉 is finite. We then go on to obtain further consequences of this result.
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05 November 2022
A Correction to this paper has been published: https://doi.org/10.1007/s44146-022-00036-9
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Communicated by Á. Szendrei
Some of the preparation of this paper occurred while the authors were guests of Johannes Kepler Universität Linz in Austria in May, 2017. The authors thank the University for its hospitality and are pleased to acknowledge partial support from the Austrian Science Fund FWF (P29931) for this visit.
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Peterson, G.L., Scott, S.D. Finiteness of the nearring of congruence preserving and 0-preserving functions of an expanded group. ActaSci.Math. 84, 401–411 (2018). https://doi.org/10.14232/actasm-017-299-9
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DOI: https://doi.org/10.14232/actasm-017-299-9