Definition:Unit of Ring/Definition 2
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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 divisor of $1_R$.
Also known as
Some sources use the term invertible element for unit of ring.
Also see
Sources
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $6$: Polynomials and Euclidean Rings: $\S 26$. Divisibility