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Uni-soft structure applied to ordered semigroups
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DOI：10.1007/s00500-015-1837-8.png)
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Abstract
En 中文
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.
Keywords:
Ordered semigroups
Semisimple ordered semigroups
Left (resp right, two-sided, interior, quasi-, and bi-) ideal in ordered semigroups
Soft sets
Uni-soft left (resp right, two-sided, interior, quasi-, and bi-) ideals
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