TY - JOUR
ID - 4813
TI - Nearrings of functions without identity determined by a single subgroup
JO - Journal of Algebra and Related Topics
JA - JART
LA - en
SN - 2345-3931
AU - Cannon, G. Alan
AU - Enlow, V.
AD - Department of Mathematics,
Southeastern Louisiana University,
SLU 10687
Hammond, LA 70402,
USA
AD - Department of Mathematics,
Southeastern Louisiana University
Hammond, LA 70402,
USA
Y1 - 2021
PY - 2021
VL - 9
IS - 1
SP - 121
EP - 129
KW - Abelian
KW - distributive
KW - center
KW - ideal
KW - zero-symmetric
DO - 10.22124/jart.2021.15730.1190
N2 - 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 $M$.
UR - https://jart.guilan.ac.ir/article_4813.html
L1 - https://jart.guilan.ac.ir/article_4813_288624afb20502195541c69de3b63864.pdf
ER -