KU代数上的(∈,∈∨q(λ,μ))-模糊正关联理想

摘要

给出了KU代数的点态化(∈,∈∨q(λ,μ))-模糊正关联理想与广义模糊正关联理想的概念,得到了KU代数的(∈,∈∨q(λ,μ))-模糊正关联理想的一些等价刻画,并指出了(∈,∈∨q(λ,μ))-模糊正关联理想有丰富的层次结构;其次得到了多个KU代数的(∈,∈∨q(λ,μ))-模糊正关联理想的交、并、同态像和同态原像(在一定条件下)也是(∈,∈∨q(λ,μ))-模糊正关联理想;而后又对KU代数(∈,∈∨q(λ,μ))-模糊正关联理想的直积以及投影进行了研究;最后给出KU代数的正关联理想的降(升)链条件的新概念,并利用(∈,∈∨q(λ,μ))-模糊正关联理想的性质研究了KU代数的正关联理想的降(升)链条件.%Firstly, this paper gives the concepts of pointwise (∈,∈∨q(λ,μ))-fuzzy positive implicative ideals and gen-eralized fuzzy positive implicative ideals of KU-algebras, obtains some equivalent characterizations of (∈,∈∨q(λ,μ))-fuzzy positive implicative ideals of KU-algebras, and points the richer hierarchical structure of the fuzzy positive implicative ideals. Secondly, this paper acquires the properties that intersections, unions, homomorphic image and homomorphic preimage (under certain condition) of (∈,∈∨q(λ,μ))-fuzzy positive implicative ideals of KU-algebras are also (∈,∈∨q(λ,μ))-fuzzy positive implicative ideals. Then, this paper investigates the direct product and proje-ction of (∈,∈∨q(λ,μ))-fuzzy positive implicative ideals of KU-algebras. At last, this paper introduces the new con-cepts of the descending (ascending) chain conditions of the positive implicative ideals of KU-algebras, which are studied by using the properties of (∈,∈∨q(λ,μ))-fuzzy positive implicative ideals.