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.

Relation with other properties

Stronger properties

• Normal subloop
• Subloop whose left cosets are pairwise disjoint