Right inverse property loop

This article defines a property that can be evaluated for a loop.
View other properties of loops

Definition

An algebra loop $(L,*)$ is termed a right inverse property loop or right inverse loop or RIP-loop if there exists a map $\rho :L\to L$ such that, for all $a,b\in L$, we have:

$\!(a*b)*\rho (b)=a$

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
Group				|FULL LIST, MORE INFO
Inverse property loop				|FULL LIST, MORE INFO
Right Bol loop				|FULL LIST, MORE INFO
Right Bruck loop				|FULL LIST, MORE INFO