Definition:Unit of Ring/Definition 1

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Not to be confused with Definition:Unity of Ring.

Definition

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


Sources