Some matrix completions over integral domains

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• 作者：Grigore Călugăreanu ^{calu@math.ubbcluj.ro" class="auth_mail" title="E-mail the corresponding author}
• 关键词：16U60 ; 16U99
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：15 October 2016
• 年：2016
• 卷：507
• 期：Complete
• 页码：414-419
• 全文大小：223 K

文摘

We characterize 3×3$3\times 3$ nilpotent matrices which are completions of 2×2$2\times 2$ arbitrary matrices and 3×3$3\times 3$ idempotent matrices which are completions of 2×2$2\times 2$ arbitrary matrices over integral domains. As an application we show that a nil-clean element of a ring which belongs to a corner of the ring, may not be nil-clean in this corner.