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K. P. Shum, L. Du and Y. Q. Guo, “Green’s Relations and Their Generalizations on Semigroups,” Discussiones Mathematicae —General Algebra and Applications, Vol. 30, No. 1, 2010, pp. 71-89. http://dx.doi.org/10.7151/dmgaa.1163

has been cited by the following article:

• TITLE: Applications of Homomorphism on the Structure of Semigroups

  AUTHORS: Huishu Yuan, Xiangzhi Kong

  KEYWORDS: Homomorphism; Natural Partial Order; Green’s (*, ~) -Relation; Semilattice Decomposition

  JOURNAL NAME: Advances in Pure Mathematics, Vol.4 No.2, February 28, 2014

  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.