Quotient loop

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Definition

Suppose (L,*) is an algebra loop and N is a normal subloop of L. The quotient loop L/N is defined as the following algebra loop:

  1. The set of elements of L/N is the set of left cosets of N, i.e., subsets of the form a * N, with a \in L.
  2. The multiplication is defined by (a * N) * (b * N) = (a * b) * N. That this is well-defined follows from the definition of normal subloop.