Abstract
It will be proved that every non-trivial variety \({\mathbb{V}}\) of bands (idempotent semigroups) contains a proper generating class of non-isomorphic bands B such that B generates \({\mathbb{V}}\) and any band \({B\prime}\) having the same endomorphism monoid as B is isomorphic to B or to the opposite band B op. Consequently, every sharply greater band variety has a sharply greater class of endomorphism monoids.
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Presented by P. P. Pálfy
This article is dedicated to Ervin Fried
The second author was supported by the project P202/12/G061 CE-ITI of the Grant Agency of Czech Republic.
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Goralčík, P., Koubek, V. & Sichler, J. On endomorphism monoids in varieties of bands. Algebra Univers. 76, 287–292 (2016). https://doi.org/10.1007/s00012-016-0399-7
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DOI: https://doi.org/10.1007/s00012-016-0399-7