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Jacobsons Lemma fails for nil-clean 2 × 2 integral matrices
Analele Universitatii "Ovidius" Constanta - Seria Matematica ( IF 0.8 ) Pub Date : 2020-12-01 , DOI: 10.2478/auom-2020-0035
Grigore Călugăreanu 1 , Horia F. Pop 2
Affiliation  

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.

中文翻译:

Jacobsons Lemma 对 nil-clean 2 × 2 积分矩阵失败

摘要 我们证明,对于两个 2 × 2 的积分矩阵 A、B,如果乘积 AB 是零净的,那么 BA 可能不是零净的。尽管对于许多特殊情况,BA 也是 nil-clean 的,但我们最终找到了三个反例。一路上,计算机辅助是决定性的。
更新日期:2020-12-01
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