%0 Journal Article %A Hila, Kostaq %A Davvaz, Bijan %A Naka, Krisanthi %T On Hyperideal Structure of Ternary Semihypergroups %J Iranian Journal of Mathematical Sciences and Informatics %V 9 %N 1 %U http://ijmsi.ir/article-1-575-en.html %R 10.7508/ijmsi.2014.01.008 %D 2014 %K Semihypergroup, Ternary semihypergroup, Hyperideal, Prime left hyperideal, Semiprime left hyperideal, Irreducible left hyperideal, Hyper lter, Left m-system, Left i-system, Left p-system., %X In this paper, we introduce and study the concepts of prime left, semiprime left and irreducible left hyperideals in ternary semihyper- groups and investigate some basic properties of them. We introduce the concepts of hyper lter and hypersemilattice congruence of ternary semi- hypergroups. We give some characterizations of hyper lters in ternary semihypergroups. Some relationships between hyper lters, prime hyper- ideals and hypersemilattice congruences in ternary semihypergroups are considered. We also introduce the notion of hyperideals extensions in ternary semihypergroups and some properties of them are investigated. %> http://ijmsi.ir/article-1-575-en.pdf %P 81-98 %& 81 %! %9 Research paper %L A-10-746-2 %+ %G eng %@ 1735-4463 %[ 2014