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Uni-soft structure applied to ordered semigroups

  • Methodologies and Application
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Abstract

The notions of uni-soft types of ideals, bi-ideals, quasi-ideals and interior ideals in ordered semigroups are considered. The main goal of this paper is to study some classes of ordered semigroups and to investigate some interesting characterization theorems of these classes in terms of uni-soft types of ideals. In this respect, we characterize weakly regular ordered semigroups, intra-regular and left weakly regular ordered semigroups and semisimple ordered semigroups in terms of uni-soft ideals. The characterization of semisimple ordered semigroups in terms of uni-soft ideal is considered and it is shown that every uni-soft two-sided ideal is idempotent. Furthermore, in semisimple ordered semigroups, the concepts of uni-soft two-sided ideals and uni-soft interior ideals coincide. Using the properties of uni-soft left and right ideals, the characterizations of intra-regular and weakly regular ordered semigroups are provided and it is given that every uni-soft left (right) ideal in left (right) weakly regular ordered semigroup is idempotent.

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Authors and Affiliations

  1. Department of Mathematics, Abdul Wali Khan University, Mardan, KPK, Pakistan

    Asghar Khan & Raees Khan

  2. Department of Mathematics Educations and RINS, Gyeongsang National University, Chinju, 660-701, South Korea

    Young Bae Jun

Authors
  1. Asghar Khan
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  2. Raees Khan
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  3. Young Bae Jun
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Correspondence to Asghar Khan.

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Communicated by V. Loia.

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Khan, A., Khan, R. & Jun, Y.B. Uni-soft structure applied to ordered semigroups. Soft Comput 21, 1021–1030 (2017). https://doi.org/10.1007/s00500-015-1837-8

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  • DOI: https://doi.org/10.1007/s00500-015-1837-8

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