dedekind domain
Word Rarity
Very rare
Frequency: Zipf frequency 1.72 in modern English
24
Scrabble Score
14
Letters
3
Syllables
8
Unique Chars
Meaning
noun
An integral domain in which every proper ideal factors into a product of prime ideals which is unique (up to permutations).
Example Sentences
- "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."