Representations of Symmetric Implication Algebras as Multicubes
Combinatorics
2009-02-09 v1 Rings and Algebras
Abstract
We show that the variety of symmetric implication algebras is generated from cubic implication algebras and Boolean algebras. We do this by developing the notion of a locally symmetric implication algebra that has properties similar to cubic implication algebras and provide a representation of these algebras as subalgebras of a product of a cubic implication algebra and an implication algebra. We then show that every symmetric implication algebra is covered by a locally symmetric implication algebra.
Cite
@article{arxiv.0902.0993,
title = {Representations of Symmetric Implication Algebras as Multicubes},
author = {Colin Bailey and Joseph Oliveira},
journal= {arXiv preprint arXiv:0902.0993},
year = {2009}
}
Comments
25 pages