Definition:Unit of Ring/Definition 1

From ProofWiki
Jump to navigation Jump to search
Not to be confused with Definition:Unity of Ring.


Let $\struct {R, +, \circ}$ be a ring with unity whose unity is $1_R$.

An element $x \in R$ is a unit of $\struct {R, +, \circ}$ if and only if $x$ is invertible under $\circ$.

That is, a unit of $R$ is an element of $R$ which has an inverse.

$\exists y \in R: x \circ y = 1_R = y \circ x$

Also known as

Some sources use the term invertible element for unit of ring.

Also see