• Corpus ID: 231924975

Locality and Centrality: The Variety ZG

@article{Amarilli2021LocalityAC,
  title={Locality and Centrality: The Variety ZG},
  author={Antoine Amarilli and Charles Paperman},
  journal={ArXiv},
  year={2021},
  volume={abs/2102.07724}
}
We study the variety ZG of monoids where the elements that belong to a group are central, i.e., commute with all other elements. We show that ZG is local, that is, the semidirect product ZG ∗ D of ZG by definite semigroups is equal to LZG, the variety of semigroups where all local monoids are in ZG. Our main result is thus: ZG ∗ D = LZG. We prove this result using Straubing’s delay theorem, by considering paths in the category of idempotents. In the process, we obtain the characterization ZG… 
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