Subloop

Definition
A subset of an algebra loop is termed a subloop if it satisfies the following equivalent conditions:


 * 1) It is closed under the multiplication of the algebra loop and forms an algebra loop under the induced multiplication.
 * 2) It is closed under the multiplication of the algebra loop, has the same identity element, and forms an algebra loop under the induced multiplication.

Stronger properties

 * Weaker than::Normal subloop
 * Weaker than::Subloop whose left cosets are pairwise disjoint