Definition:Integral Domain/Definition 2

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

• Equivalence of Definitions of Integral Domain

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