Editing Split exact sequence (section)

{{Short description|Type of short exact sequence in mathematics}}

The term '''split exact sequence''' is used in two different ways by different people.  Some people mean a [[short exact sequence]] that right-splits (thus corresponding to a semidirect product) and some people mean a [[short exact sequence]] that left-splits (which implies it right-splits, and corresponds to a direct product).  This article takes the latter approach, but both are in common use.  When reading a book or paper, it is important to note precisely which of the two meanings is in use.

In [[mathematics]], a '''split exact sequence''' is a [[short exact sequence]] in which the middle term is built out of the two outer terms in the simplest possible way.