2012; Physical and Mathematical Sciences, 46(3 (229): 14–16
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A FUNCTIONAL REPRESENTATION OF FREE DE MORGAN ALGEBRAS

Vahagn Aslanyan*

Received: 2025-02-18 · Published: 2012-12-01

© 2012 The Author(s) and the original publisher.

CC BY-NC 4.0 This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
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Original title
A FUNCTIONAL REPRESENTATION OF FREE DE MORGAN ALGEBRAS
Author
Vahagn Aslanyan
Published
2012-12-01
Licence
Creative Commons Attribution-NonCommercial 4.0 International
Original
https://doi.org/10.46991/PYSU:A/2012.46.3.014

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.
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