Cancellable elements of the lattice of semigroup varieties

• Published in: Algebra and Discrete Mathematics
• Date: 2018
• Main Authors: Gusev, S.V., Skokov, D.V., Vernikov, B.M.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/188372
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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.