alternative algebra oor Nederlands
alternative algebra
en
(algebra) An algebra such that every subalgebra generated by two elements is associative.
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Alternative algebras are so named because they are the algebras for which the associator is alternating.
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The converse, however, is not true, in contrast to the situation in alternative algebras.
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In abstract algebra, an alternative algebra is an algebra in which multiplication need not be associative, only alternative.
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Every associative algebra is power-associative, but so are all other alternative algebras (like the octonions, which are non-associative) and even some non-alternative algebras like the sedenions and Okubo algebras.
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Every associative algebra is obviously alternative, but so too are some strictly non-associative algebras such as the octonions.
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Conversely, any algebra whose associator is alternating is clearly alternative.
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The abstract group formulation did not apply to a large portion of 19th century group theory, and an alternative formalism was given in terms of Lie algebras.
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Every associative algebra is power-associative, but so are all other alternative algebras (like the octonions, which are non-associative) and even some non-alternative algebras like the sedenions and Okubo algebras.
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Alternatively, they may be described by polynomial equations, in which case they are called algebraic varieties, and if they additionally carry a group structure, they are called algebraic groups.
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This algebra is an alternative to the complicated process of directly deriving point estimators for complex long-run averages.
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Alternatively, they may be described by polynomial equations, in which case they are called algebraic varieties, and if they additionally carry a group structure, they are called algebraic groups.
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Some other letters concern matrix algebra on population dynamics, Markov models, Sustainable energy (title Winds of change: calculations on the power of a wind turbine), alternative equilibria.
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