半群的(∈,∈ ∨q(λ,μ))-模糊k-理想(英文)  

(∈,∈ ∨q(λ,μ))-FUZZY k-IDEALS OF SEMIGROUPS

作　　者：廖祖华[1] 易丽华[1] 胡淼菡[1] 

机构地区：[1]江南大学理学院,江苏无锡214122

出　　处：《数学杂志》2012年第2期191-205,共15页Journal of Mathematics

基　　金：Supported by Program for Innovation Research Team of Jiangnan University(200902)

摘　　要：本文研究了半群中的广义模糊k-理想和(∈,∈∨q(λ,μ))-模糊k-理想.利用模糊集的截集及模糊集的性质,获得了(∈,∈∨q(λ,μ))-模糊k-理想的等价刻画,广义模糊特征化及广义模糊k-理想直积的基本性质.最后还给出了半群S是左k-诺特的充要条件是对于S的任意广义模糊左k-理想A,Im(A)是[λ,μ]上的良序子集.这些结果有重要的理论价值.This article studies generalized fuzzy k-ideals and（∈,∈ ∨q（λ,μ））-fuzzy k-ideals in semigroups.By using the axiom method,fuzzy cut sets and the properties of fuzzy sets,we obtain the equivalent characterization of（∈,∈ ∨q（λ,μ））-fuzzy k-ideals and the fundamental properties of generalized fuzzy characteristic and the direct product of generalized fuzzy k-ideals.Finally,we discuss the k-notherian semigroups and obtain that a semigroup S is left k-notherian i？ Im（A） is a well-ordered subset of [λ,μ] for each generalized fuzzy left k-ideals A of S.

关 键 词：广义模糊k-理想 (∈ ∈∨q(λ μ))-模糊k-理想 广义模糊特征化 模糊直和 k-诺特 

分 类 号：O152.7[理学—数学] O159[理学—基础数学]