Category:Definitions/Integral Domains

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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 (from the Cancellation Law of Ring Product of Integral Domain) in which all non-zero elements are cancellable.

Subcategories

This category has the following 10 subcategories, out of 10 total.