Definition:Algebra Loop

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An algebra loop $\left({S, \circ}\right)$ is a quasigroup with an identity element.

That is:

$\exists e \in S: \forall x \in S: x \circ e = x = e \circ x$.

Also known as

Some sources refer to an algebra loop as just a loop.

Also see

  • Results about algebra loops can be found here.