Automorphisms of the endomorphism algebra of a free module

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• 作者：Jordan Courtemanche ^{Jordan_Courtemanche@baylor.edu" class="auth_mail" title="E-mail the corresponding author} ; Manfred Dugas ; ^{Manfred_Dugas@baylor.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 16W20 ; secondary ; 16S50
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：1 December 2016
• 年：2016
• 卷：510
• 期：Complete
• 页码：79-91
• 全文大小：335 K

文摘

Let R   be a commutative ring with identity 1∈R$1\in R$ and V a free R  -module of arbitrary rank. Let End_R(V)$En{d}_R(V)$ denote the R-algebra of all R-linear endomorphisms of V. We show that all R  -algebra automorphisms of End_R(V)$En{d}_R(V)$ are inner if R   is a Bezout domain. We also consider 2-local automorphisms of End_R(V)$En{d}_R(V)$.