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 $M$.
Cannon, G., & Enlow, V. (2021). Nearrings of functions without identity determined by a single subgroup. Journal of Algebra and Related Topics, 9(1), 121-129. doi: 10.22124/jart.2021.15730.1190
MLA
G. Alan Cannon; V. Enlow. "Nearrings of functions without identity determined by a single subgroup". Journal of Algebra and Related Topics, 9, 1, 2021, 121-129. doi: 10.22124/jart.2021.15730.1190
HARVARD
Cannon, G., Enlow, V. (2021). 'Nearrings of functions without identity determined by a single subgroup', Journal of Algebra and Related Topics, 9(1), pp. 121-129. doi: 10.22124/jart.2021.15730.1190
VANCOUVER
Cannon, G., Enlow, V. Nearrings of functions without identity determined by a single subgroup. Journal of Algebra and Related Topics, 2021; 9(1): 121-129. doi: 10.22124/jart.2021.15730.1190
)