Definition:Normed Ring

Definition

Let $\struct {R, +, \circ}$ be a ring.

Let $\norm {\, \cdot \,}$ be a norm on $R$.

Then $\struct {R, \norm {\, \cdot \,} }$ is a normed ring.

Also defined as

Some sources use the term normed ring to mean a Banach algebra.

Also see

• Definition:Norm on Ring
• Definition:Normed Division Ring

• Results about normed rings can be found here.