Cancellable elements of the lattice of semigroup varieties

We completely determine all commutative semigroup varieties that are cancellable elements of the lattice SEM of all semigroup varieties. In particular, we verify that a commutative semigroup variety is a cancellable element of the lattice SEM if and only if it is a modular element of this lattice.

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Veröffentlicht in:Algebra and Discrete Mathematics
Datum:2018
Hauptverfasser: Gusev, S.V., Skokov, D.V., Vernikov, B.M.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут прикладної математики і механіки НАН України 2018
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/188372
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Zitieren:Cancellable elements of the lattice of semigroup varieties / S.V. Gusev, D.V. Skokov, B.M. Vernikov // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 1. — С. 34–46. — Бібліогр.: 13 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Gusev, S.V.
Skokov, D.V.
Vernikov, B.M.
author_facet Gusev, S.V.
Skokov, D.V.
Vernikov, B.M.
citation_txt Cancellable elements of the lattice of semigroup varieties / S.V. Gusev, D.V. Skokov, B.M. Vernikov // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 1. — С. 34–46. — Бібліогр.: 13 назв. — англ.
collection DSpace DC
container_title Algebra and Discrete Mathematics
description We completely determine all commutative semigroup varieties that are cancellable elements of the lattice SEM of all semigroup varieties. In particular, we verify that a commutative semigroup variety is a cancellable element of the lattice SEM if and only if it is a modular element of this lattice.
first_indexed 2025-12-07T16:34:06Z
format Article
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1726-3255
language English
last_indexed 2025-12-07T16:34:06Z
publishDate 2018
publisher Інститут прикладної математики і механіки НАН України
record_format dspace
spelling Gusev, S.V.
Skokov, D.V.
Vernikov, B.M.
2023-02-26T12:17:33Z
2023-02-26T12:17:33Z
2018
Cancellable elements of the lattice of semigroup varieties / S.V. Gusev, D.V. Skokov, B.M. Vernikov // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 1. — С. 34–46. — Бібліогр.: 13 назв. — англ.
1726-3255
2010 MSC: Primary 20M07; Secondary 08B15
https://nasplib.isofts.kiev.ua/handle/123456789/188372
We completely determine all commutative semigroup varieties that are cancellable elements of the lattice SEM of all semigroup varieties. In particular, we verify that a commutative semigroup variety is a cancellable element of the lattice SEM if and only if it is a modular element of this lattice.
The work is partially supported by Russian Foundation for Basic Research (grant 17-01-00551) and by the Ministry of Education and Science of the Russian Federation (project 1.6018.2017).
en
Інститут прикладної математики і механіки НАН України
Algebra and Discrete Mathematics
Cancellable elements of the lattice of semigroup varieties
Article
published earlier
spellingShingle Cancellable elements of the lattice of semigroup varieties
Gusev, S.V.
Skokov, D.V.
Vernikov, B.M.
title Cancellable elements of the lattice of semigroup varieties
title_full Cancellable elements of the lattice of semigroup varieties
title_fullStr Cancellable elements of the lattice of semigroup varieties
title_full_unstemmed Cancellable elements of the lattice of semigroup varieties
title_short Cancellable elements of the lattice of semigroup varieties
title_sort cancellable elements of the lattice of semigroup varieties
url https://nasplib.isofts.kiev.ua/handle/123456789/188372
work_keys_str_mv AT gusevsv cancellableelementsofthelatticeofsemigroupvarieties
AT skokovdv cancellableelementsofthelatticeofsemigroupvarieties
AT vernikovbm cancellableelementsofthelatticeofsemigroupvarieties