A Subclass of Ockham Algebras  

作　　者：Jie FANG Zhong Ju SUN 

机构地区：[1]School of Computer Science,Guangdong Polytechnic Normal University

出　　处：《Acta Mathematica Sinica,English Series》2012年第10期2115-2128,共14页数学学报（英文版）

摘　　要：Here we introduce a subclass of the class of Ockham algebras （L; f） for which L satisfies the property that for every x ∈ L, there exists n 〉 0 such that fn（x） and f^n＋1（x） are complementary. We characterize the structure of the lattice of congruences on such an algebra （L; f）. We show that the lattice of compact congruences on L is a dual Stone lattice, and in particular, that the lattice Con L of congruences on L is boolean if and only if L is finite boolean. We also show that L is congruence coherent if and only if it is boolean. Finally, we give a sufficient and necessary condition to have the subdirectly irreducible chains.Here we introduce a subclass of the class of Ockham algebras （L; f） for which L satisfies the property that for every x ∈ L, there exists n 〉 0 such that fn（x） and f^n＋1（x） are complementary. We characterize the structure of the lattice of congruences on such an algebra （L; f）. We show that the lattice of compact congruences on L is a dual Stone lattice, and in particular, that the lattice Con L of congruences on L is boolean if and only if L is finite boolean. We also show that L is congruence coherent if and only if it is boolean. Finally, we give a sufficient and necessary condition to have the subdirectly irreducible chains.

关 键 词：Boolean algebra Ockham algebra CONGRUENCE congruence coherence subdirectly irre-ducible 

分 类 号：O153[理学—数学]