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Dedekind domain

noun

Etymology

Named after German mathematician Richard Dedekind (1831–1916).

Definitions

  1. An integral domain in which every proper ideal factors into a product of prime ideals…

    An integral domain in which every proper ideal factors into a product of prime ideals which is unique (up to permutations).

    • It can be proved that a Dedekind domain (as defined above) is equivalent to an integral domain in which every proper fractional ideal is invertible.
    • In this chapter we shall study several of the important classes of rings which contain the class of Dedekind domains.
    • As we can see every principal ideal domain is a Dedekind domain.

The neighborhood

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