On Generalised Quasi-ideals in Ordered Ternary Semigroups
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In this paper, we introduce generalised quasi-ideals in ordered ternary semigroups. Also, we define ordered $m$-right ideals, ordered $(p, q)$-lateral ideals and ordered $n$-left ideals in ordered ternary semigroups and studied the relation between them. Some intersection properties of ordered $(m, (p, q), n)$-quasi ideals are examined. We also characterize these notions in terms of minimal ordered $(m, (p, q), n)$-quasi-ideals in ordered ternary semigroups. Moreover, $m$-right simple, $(p, q)$-lateral simple, $n$-left simple, and $(m,(p, q), n)$-quasi simple ordered ternary semigroups are defined and some properties of them are studied.
Abstract
In this paper, we introduce generalised quasi-ideals in ordered ternary semigroups. Also, we define ordered $m$-right ideals, ordered $(p, q)$-lateral ideals and ordered $n$-left ideals in ordered ternary semigroups and studied the relation between them. Some intersection properties of ordered $(m, (p, q), n)$-quasi ideals are examined. We also characterize these notions in terms of minimal ordered $(m, (p, q), n)$-quasi-ideals in ordered ternary semigroups. Moreover, $m$-right simple, $(p, q)$-lateral simple, $n$-left simple, and $(m,(p, q), n)$-quasi simple ordered ternary semigroups are defined and some properties of them are studied.
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