Category:Definitions/Integral Domains

This category contains definitions related to Integral Domains.
Related results can be found in Category:Integral Domains.

An integral domain $\struct {D, +, \circ}$ is:

a commutative ring which is non-null

with a unity

in which there are no (proper) zero divisors, that is:

$\forall x, y \in D: x \circ y = 0_D \implies x = 0_D \text{ or } y = 0_D$

that is, in which all non-zero elements are cancellable.