ACTA issues

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

Gary L. Peterson, Stuart D. Scott

Acta Sci. Math. (Szeged) 84:3-4(2018), 401-411

Abstract. In this paper we shall obtain that the nearring $C_0(V)$ 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, $C_0(V)$ of an expanded group $\langle V,+,F\rangle $ is finite when the nearring of 0-preserving polynomial functions $P_0(V)$ of $\langle V,+,F\rangle $ is finite. We then go on to obtain further consequences of this result.

DOI: 10.14232/actasm-017-299-9

AMS Subject Classification (1991): 16Y30; 08A40

Keyword(s): nearring, expanded group, tame module, polynomial functions, congruence preserving functions, endomorphism nearring

Received July 10, 2017 and in final form May 20, 2018. (Registered under 49/2017.)