# 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.

## Source of Name

This entry was named for Joe Lee Dorroh.