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.
出处
《数学杂志》
CSCD
北大核心
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)
作者简介
廖祖华(1957-),male,born at Nanchang,Jiangxi,professor,major in matrix theory,fuzzy and rough algebra.E-mail:liaozuhua57@yahoo.cn.
