The complete principal divisor lattices  

作　　者：WANG XuePing & QU XiaoBing College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,China 

出　　处：《Science China Mathematics》2010年第8期2159-2172,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.10671138)

摘　　要：In this paper,we introduce a concept of principal divisor lattice and describe the structure of its elements.We first give a necessary and sufficient condition for the existence of irredundant join irreducible decompositions in complete principal divisor distributive lattices,and prove that the complete lower continuous,principal divisor lattices have irredundant join irreducible decompositions.In the end,we show the descriptions of lattices that have unique(resp.replaceable) irredundant join irreducible decompositions in complete lower continuous principal divisor lattices.In this paper,we introduce a concept of principal divisor lattice and describe the structure of its elements.We first give a necessary and sufficient condition for the existence of irredundant join irreducible decompositions in complete principal divisor distributive lattices,and prove that the complete lower continuous,principal divisor lattices have irredundant join irreducible decompositions.In the end,we show the descriptions of lattices that have unique(resp.replaceable) irredundant join irreducible decompositions in complete lower continuous principal divisor lattices.

关 键 词：COMPLETE LATTICE principal DIVISOR LATTICE DISTRIBUTIVE LATTICE irredundant join IRREDUCIBLE decomposition 

分 类 号：O157.5[理学—数学]