# Special Types of Rings

**1.** __Commutative Rings__:

A ring is said to be a commutative, if the multiplication composition in is commutative. i.e.

**2.** __Rings with Unit Element__:

A ring is said to be a ring with unit element if has a multiplicative identity, i.e. if there exist an element denoted by , such that

The ring of all matrices with element as integers (rational, real or complex numbers) is a ring with unity. The unity matrix

is the unity element of the ring.

**3.** __Rings with or without Zero Divisors__:

While dealing with an arbitrary ring , we may find elements and in neither of which is zero, and their product may be zero. We call such elements divisors of zero or zero divisors.

__Definition__**: **

A ring element is called a divisor of zero if there exist an element in the ring such that either

or

We also say that a ring is without zero divisors if the product of no two non-zero elements of same is zero, i.e. if

either or or both and