一类新的逻辑代数—伪NM代数

A New Class of Logical Algebras—Pseudo NM-algebras

提出了一类逻辑代数一伪 NM 代数,详细地探讨了伪 NM 代数的基本性质,给出了伪 NM 代数的等价刻画,从而证明了伪 NM 代数类是一个簇。引入并研究了伪 NM 代数的滤子理论,建立了伪 NM 代数的素滤子定理及其推论等等,这些结果均可看作是 NM 代数的相应结论的非交换推广并为研究伪 NM 逻辑提代数基础。

A class of pseudo logical algebras-pseudo NM algebras are proposed and their properties are investigated in detail. The characterizations of pseudo NM algebras are obtained, and so it shows that the class of pseudo NM algebras is a variety. We also introduce and begin to study the filter theory of pseudo NM algebras, and establish the prime filter theorem of pseudo NM algebras and its some corollaries et al. All these results can be seen as non-commutative generalizations of the corresponding ones in NM algebras and provide an algebraic foundation of studying pseudo NM algebras.