Chain varieties of monoids

被引:0
|
作者
Gusev, Sergey, V [1 ]
Vernikov, Boris M. [1 ]
机构
[1] Ural Fed Univ, Inst Nat Sci & Math, Lenina 51, Ekaterinburg 620000, Russia
关键词
monoid; variety; lattice of varieties; chain; APERIODIC MONOIDS; CROSS VARIETIES; LATTICES;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A variety of universal algebras is called a chain variety if its subvariety lattice is a chain. Non-group chain varieties of semigroups were completely classified by Sukhanov in 1982. Here we completely determine non-group chain varieties of monoids (referring to monoid varieties, we consider monoids as algebras with an associative binary operation and the nullary operation that fixes the identity element). Even though the lattice of all monoid varieties embeds into the lattice of all semigroup varieties, surprisingly, the classification of non-group chain varieties in the monoid case turns out to be much more complicated than in the case of semigroups.
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页码:1 / 73
页数:73
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