| F-Covers for Right Type-A Semigroups |
| Received:December 26, 2008 Revised:May 17, 2009 |
| Key Words:
right type-$A$ semigroup $F$-rpp semigroup left cancellative monoid $\mathcal{L}^*$-homomorphism $*$-homomorphism $F$-cover.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10961014), the Natural Science Foundation of Jiangxi Province (Grant No.2008GZ048), the Science Foundation of the Education Department of Jiangxi Province and the Foundation of Jiangxi Normal University (Grant No.[2007]134) and the Graduate Innovation Special Foundation of the Education Department of Jiangxi Province (Grant No.YC08A044). |
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| Abstract: |
| A right adequate semigroup of type $F$ is defined as a right adequate semigroup which is an $F$-rpp semigroup. A right adequate semigroup $T$ of type $F$ is called an $F$-cover for a right type-$A$ semigroup $S$ if $S$ is the image of $T$ under an ${\cal L}^*$-homomorphism. In this paper, we will prove that any right type-$A$ monoid has $F$-covers and then establish the structure of $F$-covers for a given right type-$A$ monoid. Our results extend and enrich the related results for inverse semigroups. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.05.003 |
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