Retract of a loop

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