Baer alternating loop ring: Difference between revisions

Latest revision as of 01:26, 3 August 2013

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Definition

An alternating loop ring $L$ with multiplication $*$ is termed a Baer alternating loop ring if it satisfies the following two conditions:

The subring generated by any two elements is a 2-Engel Lie ring: addition forms a group, and any triple product is zero.
It is uniquely 2-divisible, i.e., the additive loop is powered over the prime 2.

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	# The subring generated by any two elements is a [[2-Engel Lie ring]]: addition forms a group, and any triple product is zero.		# The subring generated by any two elements is a [[2-Engel Lie ring]]: addition forms a group, and any triple product is zero.
	# It is uniquely 2-divisible, i.e., the additive loop is [[powered ~~group~~ for a set of primes\|powered over]] the prime 2.		# It is uniquely 2-divisible, i.e., the additive loop is [[powered loop for a set of primes\|powered over]] the prime 2.