The Variety Generated by A(T) -- Two Counterexamples
Rings and Algebras
2019-06-07 v2
Abstract
We show that V(A(T)) does not have definable principal subcongruences or bounded Maltsev depth. When the Turing machine T halts, V(A(T)) is an example of a finitely generated semilattice based (and hence congruence meet-semidistributive) variety with only finitely many subdirectly irreducible members, all finite. This is the only known example of a variety with these properties that does not have definable principal subcongruences or bounded Maltsev depth.
Keywords
Cite
@article{arxiv.1304.4659,
title = {The Variety Generated by A(T) -- Two Counterexamples},
author = {Matthew Moore},
journal= {arXiv preprint arXiv:1304.4659},
year = {2019}
}