• Title/Summary/Keyword: ordered lateral ideal

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On Ordered Ternary Semigroups

  • Daddi, Vanita Rohit;Pawar, Yashashree Shivajirao
    • Kyungpook Mathematical Journal
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    • v.52 no.4
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    • pp.375-381
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    • 2012
  • We introduce the concepts of ordered quasi-ideals, ordered bi-ideals in an ordered ternary semigroup and study their properties. Also regular ordered ternary semigroup is defined and several ideal-theoretical characterizations of the regular ordered ternary semigroups are furnished.

CHARACTERIZING THE MINIMALITY AND MAXIMALITY OF ORDERED LATERAL IDEALS IN ORDERED TERNARY SEMIGROUPS

  • Iampan, Aiyared
    • Journal of the Korean Mathematical Society
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    • v.46 no.4
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    • pp.775-784
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    • 2009
  • In 1932, Lehmer [4] gave the definition of a ternary semigroup. We can see that any semigroup can be reduced to a ternary semigroup. In this paper, we give some auxiliary results which are also necessary for our considerations and characterize the relationship between the (0-)minimal and maximal ordered lateral ideals and the lateral simple and lateral 0-simple ordered ternary semigroups analogous to the characterizations of minimal and maximal left ideals in ordered semigroups considered by Cao and Xu [2].

On Generalised Quasi-ideals in Ordered Ternary Semigroups

  • Abbasi, Mohammad Yahya;Khan, Sabahat Ali;Basar, Abul
    • Kyungpook Mathematical Journal
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    • v.57 no.4
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    • pp.545-558
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    • 2017
  • 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.