Meaning of Dedekind domain | Babel Free

Definitions

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

Equivalents

Examples

“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.”

“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.”

CEFR level