Nonempty alternative quasigroup equals alternative loop
This article gives a proof/explanation of the equivalence of multiple definitions for the term alternative loop
View a complete list of pages giving proofs of equivalence of definitions
The following are equivalent for a quasigroup:
- It is nonempty and is an alternative magma under its multiplication.
- It is an alternative loop, i.e., it is an algebra loop and is an alternative magma under its multiplication.