2014•Advances in Pure MathematicsOpen access

Applications of Homomorphism on the Structure of Semigroups

Huishu Yuan, Xiangzhi Kong

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.

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Key concepts: Semilattice, Mathematics, Homomorphism, Congruence (geometry), Special classes of semigroups, Semigroup, Pure mathematics, Discrete mathematics