Loop conditions with strongly connected graphs
Logic
2018-10-09 v1 Combinatorics
Abstract
We prove that the existence of a term satisfying in a general algebraic structure is equivalent to an existence of a term satisfying . As a consequence of a general version of this theorem and previous results we get that each strongly connected digraph of algebraic length one, which is compatible with an operation satisfying an identity of the from , has a loop.
Cite
@article{arxiv.1810.03177,
title = {Loop conditions with strongly connected graphs},
author = {Miroslav Olšák},
journal= {arXiv preprint arXiv:1810.03177},
year = {2018}
}