双重Stone代数的O理想

O-Ideal on Double Stone Algebras

理想是刻画代数结构的工具,借助理想有助于了解代数的内部结构。在分配格代数中,将运算融入格理想,衍生出核理想。核理想是认识序代数及其同余关系的载体。O理想是一类特殊的核理想,首先在双重Stone代数的基础上,引入O理想的概念,结合双重Stone代数的运算属性,构造出一类具体的O理想;其次,利用双重Stone代数核理想和余核滤子同余关系表达式,给出了由核理想寻找余核滤子的方法,获得了双重Stone代数的核理想成为O理想的充要条件。所得结论为其他分配格代数类O理想性质的研究提供了方法,丰富了分配格理论,为进一步研究分配格类的代数结构提供理论支持。

Ideal is an instrument for the characterization of algebraic structure. With the help of ideals,it helps to understand the internal structure of algebra. In the distribution lattice algebras,The operation is intergrated into the lattice ideals,and the kernel ideals is derived. The kernel ideal is the carrier of knowing of the order algebra and its congruence relations. O-ideal is a special kind of kernel ideal. Firstly,on double Stone algebras,introducing the concept of O-ideal and combining the operation attributes of double Stone algebras,a class of specific O-ideal is constructed. Secondly,with the help of congruence expressions of kernel ideal and cokernel filter,a method of searching the cokernel filter is given by using the double Stone algebra kernel ideal. The necessary and sufficient condition for the kernel ideal of a double Stone algebra to be a O-ideal is obtained. The conclusions provide a method for the study of O-ideal properties of other distributive lattice algebras,enrich the theory of distributive lattice and provide theoretical support for further study of the algebraic structure of the class of distributive algebra.