| On Radicals of Ideals of Ordered Semigroups |
| Received:September 01, 2008 Revised:January 05, 2009 |
| Key Words:
ordered semigroup ideal archimedean ($r$-archimedean, $t$-archimedean) ordered semigroup semilattice radical of an ideal.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10961014), the Natural Science Foundation of Guangdong Province (Grant No.0501332), the Excellent Youth Talent Foundation of Anhui Province (Grant No.2009SQRZ149) and the Youth Foundation of Fuyang Normal College (Grant No.2008LQ11). |
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| Abstract: |
| Let $S$ be an ordered semigroup. In this paper, we characterize ordered semigroups in which the radical of every ideal (right ideal, bi-ideal) is an ordered subsemigroup (resp., ideal, right ideal, left ideal, bi-ideal, interior ideal) by using some binary relations on $S$. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.06.013 |
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