Conference abstracts
Session S05 - Rings and Algebras
No date set
Commutative power-associative nilalgebras and Albert's problem
Elkin Quintero Vanegas
IME - USP, Brasil - eoquinro@ime.usp.br
Albert's problem ask if every commutative power-associative nilalgebra is solvable. We proof that commutative power-associative nilalgebras of dimension $n$ and nilindex $n-3$ over a field algebraically closed of characteristic zero are solvable. Finally, we study commutative power-associative nilalgebras of dimension 9 and we proof that they are solvable too.
Joint work with Juan Carlos Gutierrez Fernandez (IME - USP).