摘要
本文在J.Shsan与M.palasinski得到的关于BCK下半格中理想的既约分解与质分解的基础上,又得到了如下新结论;1.BCK—代数(不要求是下半格)的每个理想均可表示为一些既约理想的交。2.满足理想的降链条件的BCK—代数中,每个理想均有既约分解。3.满足理想的降链条件的BCK—下半格中,每个理想均有极小质分解且这种分解是唯一的。并且,以上结论亦可移植到对偶理想上。
In this paper ,We obtain the follow new results of decomposition of ideal in BCK-algebra: 1.Let (X, * ,0)be BCK-algebra,then every ideal can be written as a cross of some reduced ideals of X. 2. Let(X, * , 0)be BCK-algebra with dcc of idead. then every ideal has reduced decomposition 3.Let(X, * , 0)be BCK-lower lattice with DCC of ideal,then every ideal has minimal prime decomposition and be uniqul.
