Special elements of the lattice of epigroup varieties

被引：6
|
作者：
Shaprynskii, Vyacheslav Yu. [1 ]
Skokov, Dmitry V. [1 ]
Vernikov, Boris M. [1 ]
机构：
[1] Ural Fed Univ, Inst Math & Comp Sci, Lenina Str 51, Ekaterinburg 620000, Russia
来源：
ALGEBRA UNIVERSALIS | 2016年 / 76卷 / 01期
基金：
俄罗斯基础研究基金会;
关键词：
epigroup; variety of epigroups; lattice; neutral element; modular element; upper-modular element; MODULAR ELEMENTS; SEMIGROUP;
D O I：
10.1007/s00012-016-0380-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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：30
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