Endomorphisms of the lattice of epigroup varieties

被引：6
|
作者：
Gusev, S. V. [1 ]
Vernikov, B. M. [1 ]
机构：
[1] Ural Fed Univ, Inst Math & Comp Sci, Lenina 51, Ekaterinburg 620000, Russia
来源：
SEMIGROUP FORUM | 2016年 / 93卷 / 03期
基金：
俄罗斯基础研究基金会;
关键词：
Epigroup; Variety; Lattice of varieties; Variety of epigroups of finite degree;
D O I：
10.1007/s00233-016-9825-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider epigroups as algebras with two operations (multiplication and pseudoinversion) and construct a countably infinite family of injective endomorphisms of the lattice of all epigroup varieties. An epigroup variety is said to be a variety of finite degree if all its nilsemigroups are nilpotent. We characterize epigroup varieties of finite degree in the language of identities and in terms of minimal forbidden subvarieties.
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页码：554 / 574
页数：21
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