摘要
有界BCK-代数<X;*;0>的一个子集D叫做一个对偶理想,如果它满足(1)1∈D;(2)N(Ny*Nx)∈D和x∈D蕴涵y∈D,x,y∈X.X的一个对偶理想D有一个既约(质)分解,如果D是有限多个既约(质)对偶理想的交。本文证明下述结果:如果有界BCK-代数X的每一个对偶理想是有限生成的,则X的每个对偶理想有一个既约分解;如果有界BCK-上半格<X;*;0>的每个对偶理想是有限生成的,则X的每个对偶理想有一个质分解.
A subset D of a bounded BCK-algebra <X;* ,0> is called a dual ideal if it satisfies:(1).1∈D;(2) N(Ny* Nx)∈D and x∈D) imply y∈D for all x and y of X. A dual ideal D in X has an irreducible (prime) decomposition if D can be represented as an intersection of a finite number of irreducible (prime) dual ideals of X. In this paper, We prove the following results. If every dual ideal of a bounded BCK-algebea X is finitely generated, then every dual ideal of X has an irreducible decomposition. If every dual ideal of a bounded upper BCK-semilattice <X; * , 0> is finitely generated, then every proper dual ideal of X has a prime decomposition.
出处
《西北大学学报（自然科学版）》
CAS
CSCD
1990年第2期1-6,共6页
Journal of Northwest University（Natural Science Edition）
关键词
既约分解
分解
BCK-代数
对偶理想
Irreducible decomposition
Prime decomposition
Minimal prime decomposition
Dual ideal
