Upper-modular and related elements of the lattice of commutative semigroup varieties

被引：1

作者：

Vernikov, B. M. ^{[1
]}

机构：

[1] Ural Fed Univ, Inst Math & Comp Sci, Lenina 51, Ekaterinburg 620000, Russia

来源：

SEMIGROUP FORUM | 2017年 / 94卷 / 03期

基金：

俄罗斯基础研究基金会;

关键词：

Semigroup; Variety; Lattice of varieties; Upper-modular element; Codistributive element; Costandard element;

D O I：

10.1007/s00233-016-9843-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We completely determine upper-modular, codistributive and costandard elements in the lattice of all commutative semigroup varieties. In particular, we prove that the properties of being upper-modular and codistributive elements in the mentioned lattice are equivalent. Moreover, in the nil-case the properties of being elements of all three types turn out to be equivalent.

引用

页码：696 / 711

页数：16

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