Iranian Mathematical Society Journal of the Iranian Mathematical Society 2717-1612 3 1 2022 01 01 Centralizer nearrings 11 21 162441 10.30504/jims.2022.362376.1074 EN G. L Walls Department of Mathematics Southeastern Louisiana University Journal Article 2022 09 16 Suppose that $(G,+)$ is a group (possibly nonabelian) and that $X$ is a submonoid of the monoid of all endomorphisms of $G$ under the operation of composition of functions, $({\rm End}~{G}, \circ)$. We define the $X$-centralizer nearring of $G$ by $X$ by saying that $M_X(G):=\{ f:G \to G \mid f(0_G)=0_G \text{ and } f \circ \alpha=\alpha \circ f \text{ for all } \alpha \in X \}$. This set of functions, $M_X(G)$, is a nearring under the ``usual" operations of function ``addition" and ``composition" of functions. This paper investigates how centralizer nearrings can be defined and investigates their ideals when $X$ is a group of automorphisms. https://jims.ims.ir/article_162441_9d30a58834b5eaeb6a961b5ba7c861ef.pdf