On, around, and beyond Frobenius' theorem on division algebras

被引：0

作者：

Bresar, Matej ^{[1
,2
]}

Shulman, Victor S. ^{[3
]}

机构：

[1] Univ Ljubljana, Fac Math & Phys, Ljubljana, Slovenia

[2] Univ Maribor, Fac Nat Sci & Math, Maribor, Slovenia

[3] Vologda State Univ, Dept Math, Vologda, Russia

来源：

LINEAR & MULTILINEAR ALGEBRA | 2022年 / 70卷 / 07期

关键词：

Frobenius' theorem; quaternions; division algebra; finite-dimensional algebra; Wedderburn's principal theorem; liftable roots; ELEMENTS;

D O I：

10.1080/03081087.2020.1761281

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Frobenius' Theorem states that, besides the fields of real and complex numbers, the algebra of quaternions H is the only finitedimensional real division algebra. We first give a short elementary proof of this theorem, then characterize finite-dimensional real algebras that contain either a copy of C, a copy of H, or a pair of anticommuting invertible elements through the dimensions of their (left) ideals, and finally consider the problem of lifting algebraic elements modulo ideals.

引用

页码：1369 / 1381

页数：13

共 13 条

[1]

[Anonymous], 1878, J REINE ANGEW MATH

[2] ALGEBRAIC ELEMENTS OF A BANACH ALGEBRA MODULO AN IDEAL [J].