Associative Algebras with a Distributive Lattice of Subalgebras

被引：0

作者：

Gein, A. G. ^{[1
]}

机构：

[1] Eltsin Ural Fed Univ, Ekaterinburg, Russia

来源：

ALGEBRA AND LOGIC | 2020年 / 59卷 / 05期

关键词：

lattice of subalgebras; distributive lattice; lattice of subextensions of field;

D O I：

10.1007/s10469-020-09608-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a full description of associative algebras over an arbitrary field, whose subalgebra lattice is distributive. All such algebras are commutative, their nil-radical is at most two-dimensional, and the factor algebra with respect to the nil-radical is an algebraic extension of the base field.

引用

页码：349 / 356

页数：8