论文信息 - A Characterization of De Morgan Algebras

A Characterization of De Morgan Algebras

In this note we show that every de Morgan algebra is isomorphic to a two-subset algebra, , where P is a set of pairs (X,Y) of subsets of a set I, (X,Y)⊔ (X′,Y′)=(X∩ X′,Y∪ Y′),(X,Y) ⊓ (X′,Y′)=(X∪ X′,Y∩Y′),~(X,Y)= (Y,X), 0P=(I,∅) and 1P=(∅,I). This characterization generalizes a previous result that applied only to a special type of de Morgan algebras called ternary algebras.

Janusz A. Brzozowski

[1] Garrett Birkhoff,et al. Review: Gr. C. Moisil, Recherches sur l'algebre de la logique , 1936 .

[2] Radu Negulescu,et al. A Characterization of Finite Ternary Algebras , 1997, Int. J. Algebra Comput..

[3] Zoltán Ésik,et al. A Cayley Theorem for Ternary Algebras , 1998, Int. J. Algebra Comput..

[4] Helena Rasiowa,et al. On the Representation of Quasi-Boolean Algebras , 1957 .