| On Fuzzy Quasi-Ideals of Ordered Semigroups |
| Received:January 05, 2011 Revised:August 31, 2011 |
| Key Words:
fuzzy quasi-ideal completely semiprime fuzzy quasi-ideal strongly regular ordered semigroup left simple ordered semigroup right simple ordered semigroup.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10961014), the Science and Technology Projects in Guangdong Province (Grant No.2010B010600039), the Guangdong Provincial Natural Science Foundation of China (Grant No.S2011010003681), the Anhui Provincial Excellent Youth Talent Foundation (Grant No.2012SQRL115ZD) and the University Natural Science Project of Anhui Province (Grant No.KJ2012B133) and the Fuyang Normal College Natural Science Foundation (Grant No.2007LZ01). |
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| Abstract: |
| In this paper, fuzzy quasi-ideals of ordered semigroups are characterized by the properties of their level subsets. Furthermore, we introduce the notion of completely semiprime fuzzy quasi-ideals of ordered semigroups and characterize strongly regular ordered semigroups in terms of completely semiprime fuzzy quasi-ideals. Finally, we investigate the characterizations and decompositions of left and right simple ordered semigroups by means of fuzzy quasi-ideals. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2012.05.008 |
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