| Some Characterizations of Chains of Archimedean Ordered Semigroups |
| Received:June 01, 2011 Revised:December 19, 2011 |
| Key Words:
ordered fuzzy point archimedean ordered semigroup completely semiprime fuzzy ideal weakly completely prime fuzzy ideal.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.10961014; 11271040), 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), 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, the concept of semiprimary fuzzy ideals of an ordered semigroup is introduced. Some characterizations for an ordered semigroup $S$ to be a semilattice of archimedean ordered subsemigroups are given by some binary relations on $S$ and the fuzzy radical of fuzzy ideals of $S$. Furthermore, some characterizations for an ordered semigroup $S$ to be a chain of archimedean ordered subsemigroups are also given by means of fuzzy subsets of $S$. In particular, by using the fuzzy prime radical theorem of ordered semigroups, we prove that an ordered semigroup $S$ is a chain of archimedean ordered subsemigroups if and only if $S$ is a semilattice of archimedean ordered subsemigroups and all weakly completely prime fuzzy ideals of $S$ form a chain. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2013.02.009 |
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