Definition:Dorroh Extension

Definition
Let $R$ be a ring.

We define two operations on the cartesian product $R \times \Z$ as:
 * $\tuple {r, n} + \tuple {s ,m} = \tuple {r + s, n + m}$
 * $\tuple {r, n} \cdot \tuple {s, m} = \tuple {r s + n s + m r, n m}$

The Dorroh extension of $R$ is the ring $\struct {R \times \Z, +, \cdot}$.

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