We show that noncommutative power-associative nilalgebras of finite dimension n and nilindex k are solvable if k s n q 1 or k s n. For any given integer n ) 2, we present an example of a power-associative nilalgebra of dimension n and nilindex n y 1 which is not solvable. This implies a power-associ
On the solvability of the commutative power-associative nilalgebras of dimension 6
✍ Scribed by Ivan Correa; Irvin Roy Hentzel; Luiz Antonio Peresi
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 101 KB
- Volume
- 369
- Category
- Article
- ISSN
- 0024-3795
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✦ Synopsis
We prove that commutative power-associative nilalgebras of dimension 6 over a field of characteristic / = 2, 3, 5 are solvable.
📜 SIMILAR VOLUMES
We prove that commutative power associative nilalgebras of nilindex n and dimension n are nilpotent of index n. We find a necessary and sufficient condition for such an algebra to be a Jordan algebra and give all corresponding isomorphism classes.
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;
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Given an index set X, a collection ނ of subsets of X all of the same cardinality , Ä 4 and a collection l of commuting linear maps on some linear space, the x xg X Ž . family of linear operators whose joint kernel K s K ނ is sought consists of all l [ Ł l with A any subset of X which intersects