Loop conditions with strongly connected graphs

Miroslav Olšák

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arXiv · 1810.03177

Loop conditions with strongly connected graphs

Miroslav Olšák

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Abstract

We prove that the existence of a term $s$ satisfying $s(r,a,r,e) = s(a,r,e,a)$ in a general algebraic structure is equivalent to an existence of a term $t$ satisfying $t(x,x,y,y,z,z)=t(y,z,z,x,x,y)$. 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 $t$ satisfying an identity of the from $t(\ldots)=t(\ldots)$, has a loop.

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BibTeX RIS

Miroslav Olšák. 2018-10-07. Loop conditions with strongly connected graphs. https://arxiv.org/abs/1810.03177

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