Definition:Integral Domain/Definition 2
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Definition
An integral domain $\struct {D, +, \circ}$ is a commutative ring such that $\struct {D^*, \circ}$ is a monoid, all of whose elements are cancellable.
In this context, $D^*$ denotes the ring $D$ without zero: $D \setminus \set {0_D}$.
Also see
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): integral domain
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): integral domain