零清洁2 × 2积分矩阵的Jacobsons引理失效

Pub Date : 2020-12-01 DOI:10.2478/auom-2020-0035

G. Călugăreanu, Horia F. Pop

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引用次数: 0

摘要

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

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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