License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2021.51
URN: urn:nbn:de:0030-drops-144918
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14491/
Go to the corresponding LIPIcs Volume Portal

Grosshans, Nathan

A Note on the Join of Varieties of Monoids with LI

pdf-format:
LIPIcs-MFCS-2021-51.pdf (0.7 MB)

Abstract

In this note, we give a characterisation in terms of identities of the join of V with the variety of finite locally trivial semigroups LI for several well-known varieties of finite monoids V by using classical algebraic-automata-theoretic techniques. To achieve this, we use the new notion of essentially-V stamps defined by Grosshans, McKenzie and Segoufin and show that it actually coincides with the join of V and LI precisely when some natural condition on the variety of languages corresponding to V is verified.
This work is a kind of rediscovery of the work of J. C. Costa around 20 years ago from a rather different angle, since Costa’s work relies on the use of advanced developments in profinite topology, whereas what is presented here essentially uses an algebraic, language-based approach.

BibTeX - Entry

@InProceedings{grosshans:LIPIcs.MFCS.2021.51,
  author =	{Grosshans, Nathan},
  title =	{{A Note on the Join of Varieties of Monoids with LI}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{51:1--51:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14491},
  URN =		{urn:nbn:de:0030-drops-144918},
  doi =		{10.4230/LIPIcs.MFCS.2021.51},
  annote =	{Keywords: Varieties of monoids, join, LI}
}

Keywords: Varieties of monoids, join, LI
Collection: 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)
Issue Date: 2021
Date of publication: 18.08.2021

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI