TY - JOUR
AU - Ansari, Safoora J.
AU - Pawar, Kishor F.
PY - 2024/06/30
Y2 - 2024/07/12
TI - On Primary and Regular $\Gamma$-Semihypergroups
JF - Thai Journal of Mathematics
JA - Thai J Math
VL - 22
IS - 2
SE - Articles
DO -
UR - https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/1647
SP - 311–322
AB - <p>In this paper the notions of primary and semiprimary $\Gamma$-hyperideals in $\Gamma$-semihypergroup are introduced. It is shown that if $rad.(I)$ is a maximal $\Gamma$-hyperideal of $S$ then $I$ is a semiprimary $\Gamma$-hyperideal of $S$. It is proved that a $\Gamma$-semihypergroup $S$ is semiprimary if and only if prime $\Gamma$-hyperideals of $S$ forms a chain under set inclusion. Regular set in $\Gamma$-semihypergroup and regular $\Gamma$-hypergroup are defined with several examples. Characterizations of regular $\Gamma$-semihypergroup is established in terms of left and right $\Gamma$-hyperideals.</p>
ER -