Dictionary

Dedekind domain en · NOUN

Etymology

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

Meanings

1. (qualifier:ring theory) 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.
   • As we can see every principal ideal domain is a Dedekind domain. 2007, Leonid Kurdachenko, Javier Otal, Igor Ya. Subbotin, Artinian Modules over Group Rings, Springer (Birkhäuser), page 55:
   • In this chapter we shall study several of the important classes of rings which contain the class of Dedekind domains. 1971, Max D. Larsen, Paul J. McCarthy, Multiplicative Theory of Ideals, Elsevier (Academic Press), page 201:
   • Let us recall some material about Dedekind domains from Chapters VIII and IX of Basic Algebra. A Dedekind domain is a Noetherian integral domain that is integrally closed and has the property that every nonzero prime ideal is maximal. Any Dedekind domain has unique factorization for its ideals. 2007, Anthony W. Knapp, Advanced Algebra, Springer (Birkhäuser), page 266:

Forms

Deriveds

almost Dedekind domain

Hypernyms

Noetherian domain (integral domain whose prime ideals factorise uniquely)

Synonyms

Dedekind ring (integral domain whose prime ideals factorise uniquely)

Translations (7)

de Dedekindring (integral domain whose prime ideals factorise uniquely) · pt domínio de Dedekind (integral domain whose prime ideals factorise uniquely) · fr anneau de Dedekind (integral domain whose prime ideals factorise uniquely) · pl pierścień Dedekinda (integral domain whose prime ideals factorise uniquely) · it dominio di Dedekind (integral domain whose prime ideals factorise uniquely) · it anello di Dedekind (integral domain whose prime ideals factorise uniquely) · pt anel de Dedekind (integral domain whose prime ideals factorise uniquely)

wikipedia: Richard Dedekind