In this paper,the concepts of-condensing operator and 69-condensingoperator on a semigroup are introduced.Then we describe the-condensing operatorsand the 69-condensing operators on semilattices,join-complete lattices...In this paper,the concepts of-condensing operator and 69-condensingoperator on a semigroup are introduced.Then we describe the-condensing operatorsand the 69-condensing operators on semilattices,join-complete lattices,and inversesemigroups.As an application of our results,we also show that the unary operations*:Hg→Hg-1 Hg and*:Hg→HG on the coset semigroupK(G)of a group G are-condensing operators.Consequently,a necessary and sufficient condition for theseoperators to be 69-condensing operators is given.Some further results on condensesemigroups considered by Chen et al.(Acta Math.Hung.119:281-305,2008)arediscussed and obtained in this paper.展开更多
基金the Grants of Natural Scientific Foundation of China(Nos.61572013 and 61272196).
文摘In this paper,the concepts of-condensing operator and 69-condensingoperator on a semigroup are introduced.Then we describe the-condensing operatorsand the 69-condensing operators on semilattices,join-complete lattices,and inversesemigroups.As an application of our results,we also show that the unary operations*:Hg→Hg-1 Hg and*:Hg→HG on the coset semigroupK(G)of a group G are-condensing operators.Consequently,a necessary and sufficient condition for theseoperators to be 69-condensing operators is given.Some further results on condensesemigroups considered by Chen et al.(Acta Math.Hung.119:281-305,2008)arediscussed and obtained in this paper.
