ON QUASI-TERNARY HYPERIDEALS AND BI-TERNARY HYPERIDEALS IN TERNARY HYPERSEMIRINGS

Résumé

In this article we introduce the notion of quasi-ternary hyperideal
in ternary hypersemirings which is the generalization of one-sided hyperideal
and study some properties of it. Also, we obtain some characterizations of
quasi-ternary hyperideals in a ternary hypersemiring. Again, we introduce
the notion of bi-ternary hyperideals of ternary hypersemiring and relation between
quasi-ternary hyperideals and bi-ternary hyperideals is established. We
characterize regular ternary hypersemirings in terms of of quasi-ternary hyperideals
and bi-ternary hyperideals. Lastly, we introduce the notions of prime
quasi-ternary hyperideals and semiprime quasi-ternary hyperideals in a ternary
hypersemiring.