Definition:Dorroh Extension

Definition
Let $R$ be a ring.

We define two operations on the cartesian product $R \times \Z$ as:
 * $(r,n) + (s,m) = (r+s, n+m)$
 * $(r,n) \cdot (s,m) = (rs + ns + mr, nm)$

The Dorroh extension of $R$ is the ring $(R \times \Z, +, \cdot)$.

Also known as
The Dorroh extension is also known as the unitization.

Also see

 * Dorroh Extension is Ring with Unity
 * Definition:Unitization Functor
 * Ring can be Embedded in Dorroh Extension
 * Every Ring can be Embedded in Ring with Unity