半伪补de Morgan代数的素理想及同余性质

The Prime Ideals and Congruence Properties of Demi-Pseudocomplemented de Morgan Algebras

素理想是研究序代数同余关系的一个重要工具。在半伪补de Morgan代数上引入两类素理想,以半伪补de Morgan代数本身的运算属性为基础获得了半伪补de Morgan代数上素理想的运算特征。利用素理想构造出了半伪补de Morgan代数上的一类同余关系等式,从而借助素理想集刻画半伪补de Morgan代数的每一个同余关系,获得了半伪补de Morgan代数上的同余关系判别定理。得到次直不可约的半伪补de Morgan代数的结构特征,其元素个数小于或等于8。所得结论为其它序代数类理想性质的研究提供了方法,丰富了序代数的发展,为进一步研究序代数类的代数结构提供理论支持。

Prime ideals are an important tool for studying the class structure of order algebras.First,two prime ideals are introduced into the demi-pseudocomplemented de Morgan algebras,and the operation characteristics of the prime ideal on the demi-pseudocomplemented de Morgan algebras are obtained on the basis of the operation attributes of the demi-pseudocomplemented de Morgan algebra itself.Secondly,a kind of congruence equation on the demi-pseudocomplemented de Morgan algebras is constructed by using the prime ideal,and the congruence relation of the the demi-pseudocomplemented de Morgan algebras is portrayed by the prime ideal set,and the congruence relation theorem on the the demi-pseudocomplemented de Morgan algebras is obtained.Finally,we obtain the structural characteristics of the subdirectly irreducible the demi-pseudocomplemented de Morgan algebras whose elements are less than or equal to 8.The conclusion provides a method for the study of the properties of the other order algebras,and enriches the theory of ordered algebraic structures.