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Full-Text Articles in Algebra
Nilpotent Linear Transformations And The Solvability Of Power-Associative Nilalgebras, Ivan Correa, Irvin R. Hentzel, Pedro Pablo Julca, Luiz Antonio Peresi
Nilpotent Linear Transformations And The Solvability Of Power-Associative Nilalgebras, Ivan Correa, Irvin R. Hentzel, Pedro Pablo Julca, Luiz Antonio Peresi
Irvin Roy Hentzel
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.
Commutative Finitely Generated Algebras Satisfying ((Yx)X)X=0 Are Solvable, Ivan Correa, Irvin R. Hentzel
Commutative Finitely Generated Algebras Satisfying ((Yx)X)X=0 Are Solvable, Ivan Correa, Irvin R. Hentzel
Irvin Roy Hentzel
No abstract provided.
Complexity And Unsolvability Properties Of Nilpotency, Irvin R. Hentzel, David Pokrass Jacobs
Complexity And Unsolvability Properties Of Nilpotency, Irvin R. Hentzel, David Pokrass Jacobs
Irvin Roy Hentzel
A nonassociative algebra is nilpotent if there is some n such that the product of any n elements, no matter how they are associated, is zero. Several related, but more general, notions are left nilpotency, solvability, local nilpotency, and nillity. First the complexity of several decision problems for these properties is examined. In finite-dimensional algebras over a finite field it is shown that solvability and nilpotency can be decided in polynomial time. Over Q, nilpotency can be decided in polynomial time, while the algorithm for testing solvability uses a polynomial number of arithmetic operations, but is not polynomial time. Also …