| Naslov: | Products of commutators in matrix rings |
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| Avtorji: | ID Brešar, Matej (Avtor)
ID Gardella, Eusebio (Avtor)
ID Thiel, Hannes (Avtor) |
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| Datoteke: |  PDF - Predstavitvena datoteka, prenos (381,72 KB)
MD5: 7837A45086389740007351A529851B17
 URL - Izvorni URL, za dostop obiščite https://www.cambridge.org/core/journals/canadian-mathematical-bulletin/article/products-of-commutators-in-matrix-rings/10FD7B61EB100163AA3815437915BA66
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| Jezik: | Angleški jezik |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
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| Povzetek: | Let $R$ be a ring and let $n \ge 2$. We discuss the question of whether every element in the matrix ring $M_n(R)$ is a product of (additive) commutators $[x, y] = xy−yx$, for $x,y \in M_n(R)$. An example showing that this does not always hold, even when $R$ is commutative, is provided. If, however, $R$ has Bass stable rank one, then under various additional conditions every element in $M_n(R)$ is a product of three commutators. Further, if $R$ is a division ring with infinite center, then every element in $M_n(R)$ is a product of two commutators. If $R$ is a field and $a \in M_n(R)$, then every element in $M_n(R)$ is a sum of elements of the form $[a, x][a, y]$ with $x, y \in M_n(R)$ if and only if the degree of the minimal polynomial of $a$ is greater than $2$. |
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| Ključne besede: | commutators, matrix ring, division ring, Bass stable rank, L'vov–Kaplansky conjecture |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 01.06.2025 |
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| Leto izida: | 2025 |
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| Št. strani: | str. 512-529 |
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| Številčenje: | Vol. 68, iss. 2 |
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| PID: | 20.500.12556/DiRROS-22101  |
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| UDK: | 512 |
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| ISSN pri članku: | 0008-4395 |
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| DOI: | 10.4153/S0008439524000523 |
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| COBISS.SI-ID: | 222178051 |
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| Opomba: |
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| Datum objave v DiRROS: | 24.04.2025 |
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| Število ogledov: | 486 |
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| Število prenosov: | 294 |
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| Metapodatki: |    |
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