Cancellable elements of the lattice of monoid varieties

Sergey V. Gusev; Edmond W. H. Lee

doi:10.1007/s10474-021-01177-z

Cancellable elements of the lattice of monoid varieties

Sergey V. Gusev, Edmond W. H. Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The set of all cancellable elements of the lattice of semigroup varieties has recently been shown to be countably infinite. But the description of all cancellable elements of the lattice MON of monoid varieties remains unknown. This problem is addressed in the present article. The first example of a monoid variety with modular but non-distributive subvariety lattice is first exhibited. Then a necessary condition of the modularity of an element in MON is established. These results play a crucial role in the complete description of all cancellable elements of the lattice MON. It turns out that there are precisely five such elements.

Original language	American English
Pages (from-to)	156-168
Journal	Acta Mathematica Hungarica
Volume	165
Issue number	1
DOIs	https://doi.org/10.1007/s10474-021-01177-z
State	Published - Oct 2021

Funding

The first author is supported by the Ministry of Science and Higher Education of the Russian Federation (project FEUZ-2020-0016).

Funders	Funder number
Ministry of Education and Science of the Russian Federation	FEUZ-2020-0016
Ministry of Education and Science of the Russian Federation

ASJC Scopus Subject Areas

General Mathematics

Keywords

Monoid
Variety
Lattice of varieties
Cancellable element of a lattice
Modular element of a lattice

Disciplines

Mathematics

Access to Document

10.1007/s10474-021-01177-z

Cancellable Elements of the Lattice of Monoid VarietiesFinal published version, 220 KBLicense: Unspecified

Cite this

@article{b31f5e469c354de2b447c27d5bbbfbd5,

title = "Cancellable elements of the lattice of monoid varieties",

abstract = " The set of all cancellable elements of the lattice of semigroup varieties has recently been shown to be countably infinite. But the description of all cancellable elements of the lattice MON of monoid varieties remains unknown. This problem is addressed in the present article. The first example of a monoid variety with modular but non-distributive subvariety lattice is first exhibited. Then a necessary condition of the modularity of an element in MON is established. These results play a crucial role in the complete description of all cancellable elements of the lattice MON. It turns out that there are precisely five such elements.",

keywords = "Monoid, Variety, Lattice of varieties, Cancellable element of a lattice, Modular element of a lattice",

author = "Gusev, {Sergey V.} and Lee, {Edmond W. H.}",

note = "Publisher Copyright: {\textcopyright} 2021, Akad{\'e}miai Kiad{\'o}, Budapest, Hungary.",

year = "2021",

month = oct,

doi = "10.1007/s10474-021-01177-z",

language = "American English",

volume = "165",

pages = "156--168",

journal = "Acta Mathematica Hungarica",

issn = "0236-5294",

number = "1",

}

TY - JOUR

T1 - Cancellable elements of the lattice of monoid varieties

AU - Gusev, Sergey V.

AU - Lee, Edmond W. H.

PY - 2021/10

Y1 - 2021/10

N2 - The set of all cancellable elements of the lattice of semigroup varieties has recently been shown to be countably infinite. But the description of all cancellable elements of the lattice MON of monoid varieties remains unknown. This problem is addressed in the present article. The first example of a monoid variety with modular but non-distributive subvariety lattice is first exhibited. Then a necessary condition of the modularity of an element in MON is established. These results play a crucial role in the complete description of all cancellable elements of the lattice MON. It turns out that there are precisely five such elements.

AB - The set of all cancellable elements of the lattice of semigroup varieties has recently been shown to be countably infinite. But the description of all cancellable elements of the lattice MON of monoid varieties remains unknown. This problem is addressed in the present article. The first example of a monoid variety with modular but non-distributive subvariety lattice is first exhibited. Then a necessary condition of the modularity of an element in MON is established. These results play a crucial role in the complete description of all cancellable elements of the lattice MON. It turns out that there are precisely five such elements.

KW - Monoid

KW - Variety

KW - Lattice of varieties

KW - Cancellable element of a lattice

KW - Modular element of a lattice

UR - http://www.webofscience.com/wos/woscc/full-record/WOS:000692303800010

UR - http://www.scopus.com/inward/record.url?scp=85114180361&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85114180361&partnerID=8YFLogxK

U2 - 10.1007/s10474-021-01177-z

DO - 10.1007/s10474-021-01177-z

M3 - Article

SN - 0236-5294

VL - 165

SP - 156

EP - 168

JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

IS - 1

ER -

Cancellable elements of the lattice of monoid varieties

Abstract

Funding

ASJC Scopus Subject Areas

Keywords

Disciplines

Access to Document

Other files and links

Cite this