The theory of implicit operations
Rings and Algebras
2026-04-24 v2 Logic
Abstract
A family of partial functions of a class of algebras is said to be an implicit operation of when it is defined by a first order formula and it is preserved by homomorphisms. In this work, we develop the theory of implicit operations from an algebraic standpoint.
Cite
@article{arxiv.2512.14326,
title = {The theory of implicit operations},
author = {Luca Carai and Miriam Kurtzhals and Tommaso Moraschini},
journal= {arXiv preprint arXiv:2512.14326},
year = {2026}
}