Nilpotent linear transformations and the solvability of power-associative nilalgebras

✍ Scribed by Ivan Correa; Irvin Roy Hentzel; Pedro Pablo Julca; Luiz Antonio Peresi

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 305 KB
• Volume: 396
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2004.08.007

✦ Synopsis

We prove some results about nilpotent linear transformations. As an application we solve some cases of Albert's problem on the solvability of nilalgebras. More precisely, we prove the following results: commutative power-associative nilalgebras of dimension n and nilindex n -1 or n -2 are solvable; commutative power-associative nilalgebras of dimension 7 are solvable.