Retract of a loop

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This article defines a property that can be evaluated for a subloop of a loop| View other such properties
ANALOGY: This is an analogue in algebra loop of a property encountered in group. Specifically, it is a [[{{{new specific context}}} property]] analogous to the subloop property: retract
View other analogues of retract | View other analogues in algebra loops of subloop properties (OR, View as a tabulated list)

Definition

A subloop S of an algebra loop L is termed a retract of L if there is a homomorphism of loops f:L \to S such that f(s) = s for all s \in S.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Direct factor of a loop |FULL LIST, MORE INFO