Quotient loop

Definition
Suppose $$(L,*)$$ is an algebra loop and $$N$$ is a defining ingredient::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.