Some properties of hyperideals in ternary semihypergroups

摘要

Ternary semihypergroups are algebraic structures with one ternary associative hyperoperation. In this paper we give some properties of left (right) and lateral hyperideals in ternary semihypergroups. We introduce the notion of left simple, lateral simple, left (0-)simple and lateral 0-simple ternary semihypergroups and characterize the minimality and maximality of left (right) and lateral hyperideals in ternary semihypergroups. The relationship between them is investigated in ternary semihypergroups extending and generalizing the analogues results for ternary semigroups.