Question

Prove that an integral domain can be imbedded into a field

Answer 1

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Here goes your Answer ➡

The total quotient ring inverts every non-zero-divisor. It is a special case of a localization, which inverts all elements from an arbitrary (saturated) submonoid of the multiplicative group.

An integral domain is a commutative ring with an identity (1 ≠ 0) with no zero-divisors. That is ab = 0 ⇒ a = 0 or b = 0. Examples. The ring Z is an integral domain.

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