On the nilpotency of generalized alternative algebras

Pokrass, David; Rodabaugh, D. J.

doi:10.1016/0021-8693(77)90279-4

Cited by 4 publications

(4 citation statements)

References 8 publications

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“…If A is an alternative (or, in particular, an associative) finite-dimensional nil algebra, then A is nilpotent 10]. This property, namely that nil finite-dimensional algebras are nilpotent, also holds for many other classes of algebras including Jordan algebras over fields of characteristic not equal to two and others (see [10], [8]).…”

Section: Theorem 1 Withmentioning

confidence: 99%

“…Let f be a partial recursive function on N. Then f defines a partial function from V V to A in the following way. For each and j .for which f((i,j)) is defined we may let (8) vv k=l where g (f((i,j)))= (Cro,. '', ,or,).…”

Section: Iqmentioning

confidence: 99%

“…W(v,, v2," v,). The word (9) is expanded in the usual way by starting with the innermost pairs of v's and applying equation (8). Whenever a product i=0 =0 must be computed, (8) is only applied to numbers (i, j), 0 and O.…”

Section: Iqmentioning

confidence: 99%

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Complexity and Unsolvability Properties of Nilpotency

Hentzel¹,

Jacobs²

1990

SIAM J. Comput.

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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 presented is a polynomial time probabilistic algorithm for deciding left nillity. Then a problem involving algebras given by generators and relations is considered and shown to be NP-complete. Finally, a relation between local left nilpotency and a set of natural numbers that is 1-complete for the class $\Pi_{2}$ in the arithmetic hierarchy of recursion theory is demonstrated.

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Section: Theorem 1 Withmentioning

confidence: 99%

Section: Iqmentioning

confidence: 99%

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Complexity and Unsolvability Properties of Nilpotency

Hentzel¹,

Jacobs²

1990

SIAM J. Comput.

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“…Em 1975-76, Hentzel e Piacentini Cattaneo [7,8,9) melhoraram alguns dos resultados de Kleinfeld. Generalizações dos anéis alternativos foram estudados também por Pokrass e Rodabaugh [10] e vários outros autores.…”

Section: Introductionunclassified

Anéis quadráticos generalizados e álgebras de posto 3

Giuliani¹

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Neste trabalho estudamos uma classe de anéis, os anéis quadráticos generalizados, definidos por identidades polinomiais que valem para todas as álgebras quadráticas. Inicialmente, apresentamos uma sequência de implicações, de exemplos e contra-exemplos relacionando diversas classes de álgebras: alternativas, alternativas generalizadas, de Jordan não comutativas e quadráticas generalizadas. Em seguida, obtemos condições para que um anel quadrático generalizado seja alternativo, ou de Jordan não comutativa ou associativo. Finalmente, verificamos que um anel quadrático generalizado satisfaz uma condição quadrático. E como consequência disto obtemos uma caracterização dos anéis quadráticos generalizados simples, primos ou semiprimos.Consideramos também as álgebras de posto 3 e as álgebras com pseudo-composição.Usando a representação matricial do grupo simétrico, obtivemos para estas classes de álgebras as identidades polinomiais minimais, isto é, de menor grau

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The problem of definition expansion and contraction

Wos

1987

J Autom Reasoning

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On the nilpotency of generalized alternative algebras

Cited by 4 publications

References 8 publications

Complexity and Unsolvability Properties of Nilpotency

Complexity and Unsolvability Properties of Nilpotency

Anéis quadráticos generalizados e álgebras de posto 3

The problem of definition expansion and contraction

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