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A MINIMAL CONGRUENCE LATTICE REPRESENTATION FOR $\mathbb{M}_{p+1}$

Part of: Algebraic logic Algebraic structures Lattices

Published online by Cambridge University Press:  24 March 2020

ROGER BUNN ,
DAVID GROW ,
MATT INSALL Open the ORCID record for MATT INSALL [Opens in a new window]  and
PHILIP THIEM
ROGER BUNN
Affiliation:
Missouri State University, 901 South National Avenue, Springfield, MO65897, USA email RogerBunn@missouristate.edu
DAVID GROW
Affiliation:
Missouri University of Science and Technology, 202 Rolla Building, Rolla, MO65409-0020, USA email grow@mst.edu
MATT INSALL*
Affiliation:
Missouri University of Science and Technology, Mathematics & Statistics, 400 W 12th Street, Room 315 Rolla Building, Rolla, MO65409, USA email insall@mst.edu
PHILIP THIEM
Affiliation:
Missouri University of Science and Technology, 202 Rolla Building, Rolla, MO65409-0020, USA email ptt@mst.edu
*
✉insall@mst.edu
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Abstract

Let $p$ be an odd prime. The unary algebra consisting of the dihedral group of order $2p$, acting on itself by left translation, is a minimal congruence lattice representation of $\mathbb{M}_{p+1}$.

Keywords

06B15universal algebracongruence lattice representation

MSC classification

Primary: 03G10: Lattices and related structures 06B15: Representation theory 08A60: Unary algebras 08A62: Finitary algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 108 , Issue 3 , June 2020 , pp. 332 - 340
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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