TY - JOUR
AU - Kehayopulu, Niovi
PY - 2018/10/24
Y2 - 2023/11/29
TI - On Hoehnke Ideal in Ordered Semigroups
JF - European Journal of Pure and Applied Mathematics
JA - Eur. J. Pure Appl. Math.
VL - 11
IS - 4
SE -
DO - 10.29020/nybg.ejpam.v11i4.3341
UR - https://www.ejpam.com/index.php/ejpam/article/view/3341
SP - 911-921
AB - For a proper subset $A$ of an ordered semigroup $S$, we denote by $H_A(S)$ the subset of $S$ defined by $H_A(S):=\{h\in S \mbox { such that if } s\in S\backslash A, \mbox { then } s
otin (shS]\}$. We prove, among others, that if $A$ is a right ideal of $S$ and the set $H_A(S)$ is nonempty, then $H_A(S)$ is an ideal of $S$; in particular it is a semiprime ideal of $S$. Moreover, if $A$ is an ideal of $S$, then $A\subseteq H_A(S)$. Finally, we prove that if $A$ and $I$ are right ideals of $S$, then $I\subseteq H_A(S)$ if and only if $s
otin (sI]$ for every $s\in S\backslash A$. We give some examples that illustrate our results. Our results generalize the Theorem 2.4 in Semigroup Forum 96 (2018), 523--535.
ER -