DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications

Article in volume

Authors:

E.D. Schwab

Emil Daniel Schwab

University of Texas at El Paso

email: eschwab@utep.edu

Title:

A bisimple inverse monoid of quadruples of non-negative integers. The Möbius function

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Source:

Discussiones Mathematicae - General Algebra and Applications 44(1) (2024) 111-125

Received: 2022-10-10 , Revised: 2022-11-12 , Accepted: 2022-11-14 , Available online: 2023-08-23 , https://doi.org/10.7151/dmgaa.1440

Abstract:

The additive monoid of non-negative integers $\mathbb{N}$ is isomorphic to the right unit submonoid of the (bisimple) bicyclic semigroup $B=\mathbb{N}×\mathbb{N}$. The aim of this note is to construct a similar pair of monoids $(B^{\dagger}=\mathbb{N}×\mathbb{N},B^{\ddagger}=\mathbb{N}×\mathbb{N}×\mathbb{N}×\mathbb{N})$. The monoid $B^{\dagger}$ give rise to a bisimple inverse monoid $B^{\ddagger}$ of quadruples of non-negative integers like as Warne's 2-dimensional bicyclic semigroup. The links with the monoid of non-negative integers $\mathbb{N}$ and with the bicyclic semigroup may turn out to be expedient also for the computation of the corresponding Möbius functions.

Keywords:

bisimple inverse monoid, bicyclic semigroup, Möbius function

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