%0 Journal Article
%T Nearrings of functions without identity determined by a single subgroup
%J Journal of Algebra and Related Topics
%I University of Guilan
%Z 2345-3931
%A Cannon, G. Alan
%A Enlow, V.
%D 2021
%\ 06/01/2021
%V 9
%N 1
%P 121-129
%! Nearrings of functions without identity determined by a single subgroup
%K Abelian
%K distributive
%K center
%K ideal
%K zero-symmetric
%R 10.22124/jart.2021.15730.1190
%X Let $(G, +)$ be a finite group, written additively with identity 0, but not necessarily abelian, and let $H$ be a nonzero, proper subgroup of $G$. Then the set $M = \{f : G \to G\ |\ f(G) \subseteq H \ \hbox{and}\ f(0) = 0 \}$ is a right, zero-symmetric nearring under pointwise addition and function composition. We find necessary and sufficient conditions for $M$ to be a ring and determine all ideals of $M$, the center of $M$, and the distributive elements of $M$.
%U https://jart.guilan.ac.ir/article_4813_288624afb20502195541c69de3b63864.pdf