Examples, counterexamples, and structure in bounded width algebras
Rings and Algebras
2020-02-17 v2 Computational Complexity
Logic
Abstract
We study bounded width algebras which are minimal in the sense that every proper reduct does not have bounded width. We show that minimal bounded width algebras can be arranged into a pseudovariety with one basic ternary operation. We classify minimal bounded width algebras which have size at most three, and prove a structure theorem for minimal bounded width algebras which have no majority subalgebra, which form a pseudovariety with a commutative binary operation. As a byproduct of our results, we also classify minimal clones which have a Taylor term.
Cite
@article{arxiv.1909.05901,
title = {Examples, counterexamples, and structure in bounded width algebras},
author = {Zarathustra Brady},
journal= {arXiv preprint arXiv:1909.05901},
year = {2020}
}
Comments
Simplified and generalized the main results about partial semilattices