English

An addendum to "The theory of implicit operations"

Rings and Algebras 2026-01-05 v1 Logic

Abstract

In this addendum to [4], we provide a pair of counterexamples relevant to the theory of implicit operations. More precisely, we exhibit a pp expansion of a variety that fails to be a variety (although it is a quasivariety). Furthermore, we construct a sequence of varieties possessing a nonequational congruence preserving Beth companion.

Keywords

Cite

@article{arxiv.2601.00006,
  title  = {An addendum to "The theory of implicit operations"},
  author = {Luca Carai and Miriam Kurtzhals and Tommaso Moraschini},
  journal= {arXiv preprint arXiv:2601.00006},
  year   = {2026}
}

Comments

Addendum to arXiv:2512.14326