Congruence Permutable Kleene-Stone Algebras  

作　　者：LUO Congwen, WANG Gaoxia Department of Mathematics, China Three Gorges University, Yichang 443002, Hubei, China 

出　　处：《Wuhan University Journal of Natural Sciences》2010年第2期99-102,共4页武汉大学学报（自然科学英文版）

基　　金：Supported by the Science and Technology Project of Hubei Province (2006AA412C27)

摘　　要：A Kleene-Stone algebra is a bounded distributive lattice with two unary operations that make it a Kleene and a Stone algebra. In this paper, we study the properties of the prime ideals in a Kleene-Stone algebra and characterize the class of Kleene-Stone algebras that are congruence permutable by means of the dual space of a Kleene-Stone algebra and then show that a finite Kleene-Stone algebra is congruence permutable if and only if it is isomorphic to a direct product of finitely many simple algebras.A Kleene-Stone algebra is a bounded distributive lattice with two unary operations that make it a Kleene and a Stone algebra. In this paper, we study the properties of the prime ideals in a Kleene-Stone algebra and characterize the class of Kleene-Stone algebras that are congruence permutable by means of the dual space of a Kleene-Stone algebra and then show that a finite Kleene-Stone algebra is congruence permutable if and only if it is isomorphic to a direct product of finitely many simple algebras.

关 键 词：Kleene-Stone algebra Kleene-Stone space congruence permutable 

分 类 号：O153.1[理学—数学]