Special elements of the lattice of epigroup varieties

被引：0
|
作者：
Vyacheslav Yu. Shaprynskiǐ
Dmitry V. Skokov
Boris M. Vernikov
机构：
[1] Ural Federal University,Institute of Mathematics and Computer Science
来源：
Algebra universalis | 2016年 / 76卷
关键词：
epigroup; variety of epigroups; lattice; neutral element; modular element; upper-modular element; Primary: 20M07; Secondary: 08B15;
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学科分类号：
摘要：
We study special elements of three types (namely, neutral, modular and upper-modular elements) in the lattice of all epigroup varieties. Neutral elements are completely determined (it turns out that only four varieties have this property). We find a strong necessary condition for modular elements that completely reduces the problem of description of corresponding varieties to nilvarieties satisfying identities of some special type. Modular elements are completely classified within the class of commutative varieties, while upper-modular elements are completely determined within the wider class of strongly permutative varieties.
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页码：1 / 30
页数：29
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