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Applications of Homomorphism on the Structure of Semigroups

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DOI: 10.4236/apm.2014.42010    4,086 Downloads   6,617 Views  


By utilizing homomorphisms and -strong semilattice of semigroups, we show that the Green (*,~)-relation H*,~ is a regular band congruence on a r-ample semigroup if and only if it is a G-strong semilattice of completely J*,~-simple semigroups. The result generalizes Petrichs result on completely regular semigroups with Greens relation H a normal band congruence or a regular band congruence from the round of regular semigroups to the round of r-ample semigroups.

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The authors declare no conflicts of interest.

Cite this paper

H. Yuan and X. Kong, "Applications of Homomorphism on the Structure of Semigroups," Advances in Pure Mathematics, Vol. 4 No. 2, 2014, pp. 62-70. doi: 10.4236/apm.2014.42010.


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