%0 Journal Article
%T Applications of Homomorphism on the Structure of Semigroups
%A Huishu Yuan
%A Xiangzhi Kong
%J Advances in Pure Mathematics
%P 62-70
%@ 2160-0384
%D 2014
%I Scientific Research Publishing
%R 10.4236/apm.2014.42010
%X <p style=\"text-align:justify;\">
	<span><span style=\"font-family:Verdana;\">By utilizing homomorphisms and </span><span style=\"font-family:Verdana;\">-strong semilattice of semigroups, we show that the
Green (<span style=\"white-space:nowrap;\"><sub>*</sub>,~)</span></span><span style=\"font-family:Verdana;\">-relation</span> H<span style=\"white-space:nowrap;\"><span style=\"font-family:Verdana;line-height:15px;text-align:justify;\"><sup>*</sup></span><sup>,~</sup></span><span style=\"font-family:Verdana;\"> is a regular
band congruence on a </span><em>r</em><span style=\"font-family:Verdana;\">-ample semigroup if and only if it is a </span><em>G</em><span style=\"font-family:Verdana;\">-strong semilattice of completely </span>J<span style=\"text-align:justify;font-family:Verdana;line-height:15px;\"><sup>*</sup></span><sup style=\"text-align:justify;\">,~</sup><span style=\"font-family:Verdana;\">-simple semigroups. The result generalizes Petrich</span></span><span style=\"font-family:Verdana;\">¡¯</span><span style=\"font-family:Verdana;\">s result
on completely regular semigroups with Green</span><span style=\"font-family:Verdana;\">¡¯</span><span><span style=\"font-family:Verdana;\">s relation </span>H<span style=\"font-family:Verdana;\"> a normal band
congruence or a regular band congruence from the round of regular semigroups to
the round of </span><em>r</em><span style=\"font-family:Verdana;\">-ample semigroups.</span></span> 
</p>
%K Homomorphism
%K Natural Partial Order
%K Green¡¯s (*
%K ~) -Relation
%K Semilattice Decomposition
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=43378