Simple loop
This article defines a property that can be evaluated for a loop.
View other properties of loops
ANALOGY: This is an analogue in algebra loops of the group property:
View other analogues of simplicity | View other analogues in algebra loops of group properties
Definition
Symbol-free definition
An algebra loop is said to be simple if it has no proper nontrivial normal subloop. In other words, the only normal subloops are the whole loop and the trivial element.
Definition with symbols
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Analogy
The definition of simple loop generalizes, to algebra loops, the definition of simple group for groups.
Recall that a group is said to be simple if it has no proper nontrivial normal subgroup. The analogue of normal subgroup in algebra loops is normal subloop, and this explains the definition of simple loop.
Relation with other properties
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