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Applications of Homomorphism on the Structure of Semigroups
School of Science, Jiangnan University, Wuxi, China
School of Science, Jiangnan University, Wuxi, China
- 1 School of Science, Jiangnan University, Wuxi, China
- 2 School of Science, Jiangnan University, Wuxi, China
Advances in Pure Mathematics·Volume 04 (2014)·Pages 62–70·Published 24 February 2014·DOI10.4236/apm.2014.42010
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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.
KeywordsHomomorphismNatural Partial OrderGreen’s (*~) -RelationSemilattice Decomposition
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