Frugal Lazard-divided Lie ring: Difference between revisions
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{{Lazard-divided Lie ring property}} | |||
==Definition== | ==Definition== | ||
A [[Lazard-divided Lie ring]] <math>L</math> is termed '''frugal''' if the following holds: if <math>p</math> is a [[prime number]] such that <math>[[x_1,x_2],\dots,x_p] = 0</math> for all <math>x_1,x_2,\dots,x_p \in L</math>, then <math>t_p(x_1,x_2,\dots,x_p) = 0</math> for all <math>x_1,x_2,\dots,x_p \in L</math>. In some sense, the Lazard division operations are frugal in terms of departing from giving the zero value. | A [[Lazard-divided Lie ring]] <math>L</math> is termed '''frugal''' if the following holds: if <math>p</math> is a [[prime number]] such that <math>[[x_1,x_2],\dots,x_p] = 0</math> for all <math>x_1,x_2,\dots,x_p \in L</math>, then <math>t_p(x_1,x_2,\dots,x_p) = 0</math> for all <math>x_1,x_2,\dots,x_p \in L</math>. In some sense, the Lazard division operations are frugal in terms of departing from giving the zero value. | ||
Latest revision as of 22:56, 27 June 2013
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This article defines a Lazard-divided Lie ring property, i.e., a property that can be evaluated to true/false for a Lazard-divided Lie ring. The evaluation is invariant under isomorphism.
View all Lazard-divided Lie ring properties
Definition
A Lazard-divided Lie ring is termed frugal if the following holds: if is a prime number such that for all , then for all . In some sense, the Lazard division operations are frugal in terms of departing from giving the zero value.
![{\displaystyle [[x_{1},x_{2}],\dots ,x_{p}]=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bbae30b2b239188b0c317072306fa6d9f47a6b0b)
