English

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}
}
R2 v1 2026-06-22T00:01:12.574Z