Boole-De Morgan Algebras and Quasi-De Morgan Functions

In this paper we establish a Stone-type and a Birkhoff-type representation theorems for Boole-De Morgan algebras and prove that the free Boole-De Morgan algebra on n free generators is isomorphic to the Boole-De Morgan algebra of quasi-De Morgan functions of n variables. Also we introduce the concep...

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Bibliographic Details
Published in:Communications in algebra 2014-01, Vol.42 (11), p.4757-4777
Main Authors: Movsisyan, Yu. M., Aslanyan, V. A.
Format: Article
Language:English
Subjects:
Algebra
Boole-De Morgan algebra
Boolean function
De Morgan function
Disjunctive (conjunctive) normal form of quasi-De Morgan function
Free algebra
Functions (mathematics)
Generators
Mathematical analysis
Polynomials
Quasi-De Morgan function
Representations
Theorems
Zhegalkin polynomial for quasi-De Morgan function
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Summary:In this paper we establish a Stone-type and a Birkhoff-type representation theorems for Boole-De Morgan algebras and prove that the free Boole-De Morgan algebra on n free generators is isomorphic to the Boole-De Morgan algebra of quasi-De Morgan functions of n variables. Also we introduce the concept of Zhegalkin polynomials for quasi-De Morgan functions and consider the representation problem of those functions by polynomials.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2013.824459