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

Grigore Călugăreanu

Grigore Călugăreanu

Department of Mathematics, Babeş-Bolyai UniversityCluj-Napoca, Romania
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Călugăreanu, Grigore
 and 
Horia F. Pop

Horia F. Pop

Department of Computer Science, Babeş-Bolyai UniversityCluj-Napoca, Romania
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Pop, Horia F.
  
Dec 28, 2020
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Published Online: Dec 28, 2020
Page range: 83 - 88
Received: Jan 02, 2020
Accepted: Jan 17, 2020
DOI: https://doi.org/10.2478/auom-2020-0035
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© 2020 Grigore Călugăreanu et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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.

Language:
English
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3 times per year
Journal Subjects:
Mathematics, General Mathematics
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