Abstract: The concept of prime ideals of the[N(2,2,0)]algebra is introduced; with the help of fuzzy sets, the concepts of pointwise [(∈,∈∨q(λ,μ))-]fuzzy prime ideals and generalized fuzzy prime ideals are presented, and the relationship between them is discussed; some equivalent descriptions and properties of the [(∈,∈∨q(λ,μ))-]fuzzy prime ideals are obtained; some basic properties of homomorphic image and homomorphic preimage of the [(∈,∈∨q(λ,μ))-]fuzzy prime ideals are studied.

Key words: [N(2,2,0)]algebra, prime ideals, generalized fuzzy prime ideals, [(∈,∈∨q(λ,μ))-]fuzzy prime ideals, homomorphism

摘要： 在[N(2,2,0)]代数中引入了素理想的概念；利用模糊集理论，提出了点态化[(∈,∈∨q(λ,μ))-]模糊素理想和广义模糊素理想的概念，讨论了两者之间的关系；得到了[(∈,∈∨q(λ,μ))-]模糊素理想的一些等价刻画及其相关性质；研究了[(∈,∈∨q(λ,μ))-]模糊素理想同态像与同态原像的基本性质。

关键词: [N(2, 2, 0)]代数, 素理想, 广义模糊素理想, [(&isin, &isin, &or, q(&lambda, &mu, ))-]模糊素理想, 同态