Right inverse property loop

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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 Inverse property loop|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