Jacobsons Lemma fails for nil-clean 2 × 2 integral matrices

IF 0.8 4区数学 Q2 MATHEMATICS

Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica Pub Date : 2020-12-01 DOI:10.2478/auom-2020-0035

G. Călugăreanu, Horia F. Pop

引用次数: 0

Abstract

Abstract We show that for two 2 × 2 integral matrices A, B, if the product AB is nil-clean then BA may not be nil-clean. Despite the fact that for many special cases, BA is also nil-clean, we finally found three counterexamples. All the way, the computer aid was decisive.

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零清洁2 × 2积分矩阵的Jacobsons引理失效

摘要本文证明了对于两个2 × 2积分矩阵A, B，如果乘积AB是零清洁的，则BA可能不是零清洁的。尽管对于许多特殊情况，BA也是零干净的，但我们最终找到了三个反例。一直以来，计算机辅助都是决定性的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal is founded by Mirela Stefanescu and Silviu Sburlan in 1993 and is devoted to pure and applied mathematics. Published by Faculty of Mathematics and Computer Science, Ovidius University, Constanta, Romania.