Left alternative loop: Difference between revisions
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==Definition== | ==Definition== | ||
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===Symbol-free definition=== | ===Symbol-free definition=== | ||
A [[loop]] is termed a '''left-alternative loop''' if it is a [[fact about::left-alternative magma]]. | |||
===Definition with symbols=== | ===Definition with symbols=== | ||
Latest revision as of 16:11, 9 March 2010
This article defines a property that can be evaluated for a loop.
View other properties of loops
Definition
Symbol-free definition
A loop is termed a left-alternative loop if it is a Left-alternative magma (?).
Definition with symbols
An algebra loop is termed a left-alternative loop if the following identity is satisfied for all :
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Left Bol loop | left Bol implies left alternative | |FULL LIST, MORE INFO | ||
| Alternative loop | |FULL LIST, MORE INFO | |||
| Left Bruck loop | |FULL LIST, MORE INFO | |||
| Left power-alternative loop | |FULL LIST, MORE INFO |