伪补MS-代数的素理想及同余性质

The Prime Ideals and Congruence Properties of Pseudocomplemented MS-Algebras

素理想是研究Ockham代数类结构的一个重要工具。伪补MS-代数是同时具有伪补代数和MS-代数特征的一类代数。首先在伪补MS-代数上引入两类素理想,以伪补MS-代数本身的运算属性为基础获得了伪补MS-代数素理想的运算特征。其次,利用素理想构造出了伪补MS-代数上的一类同余关系等式,借助素理想集刻画伪补MS-代数的每一个同余关系,获得了伪补MS-代数上的同余关系判别定理。最后,得到次直不可约的伪补MS-代数的结构特征,其元素个数小于或等于6。所得结论为其他Ockham代数类核理想性质的研究提供了方法,丰富了Ockham代数的发展,为进一步研究Ockham代数类的代数结构提供理论支持。

Prime Ideals is an important tool for studying the class structure of Ockham algebras. Pseudocomplemented MS-algebra is a class of Algebra with the characteristics of both pseudocomplement and MS-algebra. Firstly, two prime ideals are introduced into the pseudocomplemented MS-algebra, and the operation characteristics of the prime ideal on pseudocom- plement MS-algebra are obtained on the basis of the operation attributes of pseudo complement MS-algebra itself. Secondly, a kind of congruence equation on the pseudo complement MS-algebra is constructed by using the prime ideal, and the congru- of the pseudocomplemented MS-algebra is portrayed by the prime ideal set, and the congruence relation theorem on the pseudocomplemented MS-algebra is obtained. Finally, the structural characteristics of the subdirectly irreducible pseudocomplemented MS-algebras are obtained ,and its elements are less than or equal to 6. The conclusion provids a method for the study of the properties of the other Ockham algebras, and enriched the theory of ordered algebraic structures.