Definition:Unit of Ring/Definition 2

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 divisor of $1_R$.

Also known as

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

Also see

• Equivalence of Definitions of Unit of Ring

Sources

• 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $6$: Polynomials and Euclidean Rings: $\S 26$. Divisibility