This article is cited in 9 papers

Mathematics

A functional representation of free De Morgan algebras

Yu. M. Movsisyan, V. A. Aslanyan

Chair of Algebra and Geometry of YSU, Armenia

Abstract: It is well known that free Boolean algebra on $n$ free generators is isomorphic to the Boolean algebra of Boolean functions of $n$ variables. The free distributive lattice on $n$ free generators is isomorphic to the lattice of monotone Boolean functions of $n$ variables. In this paper we introduce the concept of De Morgan function and prove that the free De Morgan algebra on $n$ free generators is isomorphic to the De Morgan algebra of De Morgan functions of $n$ variables.

Keywords: antichain, monotone Boolean function, De Morgan function, free De Morgan algebra.

Received: 23.06.2012
Accepted: 28.08.2012

Language: English