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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  

ABSTRACT

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.

Conflicts of Interest

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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