Iranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16123120220101Centralizer nearrings112116244110.30504/jims.2022.362376.1074ENG. LWallsDepartment of Mathematics
Southeastern Louisiana UniversityJournal Article20220916Suppose 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_433cef8ba62bad306c8dc4978d474b53.pdf