Applications of Homomorphism on the Structure of Semigroups ()
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 Petrich’s result
on completely regular semigroups with Green’s relation H a normal band
congruence or a regular band congruence from the round of regular semigroups to
the round of r-ample semigroups.
Share and Cite:
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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