The effect of assuming the identity as a generator on the length of the matrix algebra

被引：6
作者：
Laffey, Thomas [1 ]
Markova, Olga [2 ]
Smigoc, Helena [1 ]
机构：
[1] Univ Coll Dublin, Sch Math Sci, Dublin 4, Ireland
[2] Moscow MV Lomonosov State Univ, Fac Mech & Math, Dept Algebra, Moscow 119991, Russia
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2016年 / 498卷
基金：
爱尔兰科学基金会; 俄罗斯基础研究基金会;
关键词：
Finitely generated algebra; Lengths of Algebras; COMPLEX MATRICES; IRREDUCIBLE PAIRS; SIZE;
D O I：
10.1016/j.laa.2015.09.021
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let M-n(F) be the algebra of n x n matrices and let S be a generating set of M-n(F) as an F-algebra. The length of a finite generating set S of M-n(F) is the smallest number k such that words of length not greater than k generate M-n(F) as a vector space. Traditionally the identity matrix is assumed to be automatically included in all generating sets S and counted as a word of length 0. In this paper we discuss how the problem changes if this assumption is removed. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码：378 / 393
页数：16
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