<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We show that for two 2 <italic>×</italic> 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.</p></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.

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

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Jacobsons Lemma fails for nil-clean 2 × 2 integral matrices"}

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,...

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

Online veröffentlicht: 28. Dez. 2020

Seitenbereich: 83 - 88

Eingereicht: 02. Jan. 2020

Akzeptiert: 17. Jan. 2020

DOI: https://doi.org/10.2478/auom-2020-0035

Schlüsselwörter
nil-clean, clean, 2 × 2 matrix, principal ideal domain

© 2020 Grigore Călugăreanu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Online veröffentlicht: 28. Dez. 2020

Seitenbereich: 83 - 88

Eingereicht: 02. Jan. 2020

Akzeptiert: 17. Jan. 2020

DOI: https://doi.org/10.2478/auom-2020-0035

Schlüsselwörternil-clean, clean, 2 × 2 matrix, principal ideal domain

© 2020 Grigore Călugăreanu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Schlüsselwörter
nil-clean, clean, 2 × 2 matrix, principal ideal domain