Abstract

In this paper, several new results on the de Morgan and Kleene algebras are proposed. Firstly, several conditions that make a de Morgan algebra to be a Kleene algebra are considered.(1)A simple necessary and sufficient condition for it is given that can bring us some convenience in the study of de Morgan algebras and Kleene algebras. (2)The equivalence of eight sufficient conditions is proved. (3)It is also proved that a de Morgan algebra which satisfies one of the eight conditions is a Kleene algebra with sup W^+ and inf W^-. Secondly, the properties of the de Morgan algebras which satisfy two special conditions are explored and their relations are investigated. Thirdly, a direct and convenient method to obtain all the fixed points of a de Morgan algebra is introduced. And finally, some theorems on a complete de Morgan algebra are extended to the general case of removing the 'complete'.