Vipul: Created page with '==Definition== Let $L$ be a Lie ring and $S$ be a subset of $L$ . We say that $S$ is a '''subring''' of $L$ , or a '''Li…'

2009-07-16T16:06:04Z

Created page with '==Definition== Let <math>L</math> be a Lie ring and <math>S</math> be a subset of <math>L</math>. We say that <math>S</math> is a '''subring''' of <math>L</math>, or a '''Li…'

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==Definition==

Let <math>L</math> be a [[Lie ring]] and <math>S</math> be a subset of <math>L</math>. We say that <math>S</math> is a '''subring''' of <math>L</math>, or a '''Lie subring''', if it satisfies the following equivalent conditions:

# <math>S</math> is a subgroup of the additive group of <math>L</math> and is closed under the Lie bracket of <math>L</math>.
# <math>S</math> is a Lie ring with the addition and Lie bracket operations induced from <math>L</math>.

Subring of a Lie ring - Revision history

Vipul: Created page with '==Definition== Let L be a Lie ring and S be a subset of L. We say that S is a '''subring''' of L, or a '''Li…'

Vipul: Created page with '==Definition== Let $L$ be a Lie ring and $S$ be a subset of $L$ . We say that $S$ is a '''subring''' of $L$ , or a '''Li…'