P-Condense and LP-Condensing Operatorson Semilattices,Join-Complete Lattices and Some Inverse Semigroups  

作　　者：Yong He Wei Tian Kar Ping Shum 

机构地区：[1]School of Computer Science and Engineering,Hunan University of Science and Technology,Xiangtan 411201,Hunan,China [2]Intelligent Research Institute,SANY Heavy Industry CO.,Ltd,Changsha 410100,Hunan,China3 [3]Institute of Mathematics,Yunnan University,Kunming 650091,Yunnan,China

出　　处：《Communications in Mathematics and Statistics》2016年第4期435-447,共13页数学与统计通讯（英文）

基　　金：the Grants of Natural Scientific Foundation of China(Nos.61572013 and 61272196).

摘　　要：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.

关 键 词：P-condensing operator LP-condensing operator Upper closureoperator Join-complete congruence Join-complete lattice congruence Coset semigroup of a group 

分 类 号：O15[理学—数学]