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integral domain

noun

Definitions

  1. Any nonzero commutative ring in which the product of nonzero elements is nonzero.

    • A ring R is an integral domain if and only if the polynomial ring R#91;x#93; is an integral domain.
    • For any integral domain there can be derived an associated field of fractions.
    • For integral domains, we will use a⁻¹ to designate the multiplicative inverse of a (if it has one; since not all elements need have inverses, this notation can be used only where it can be shown that an inverse exists).

The neighborhood

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sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA