polynomial ring
Word Rarity
Rare
Frequency: Zipf frequency 3.10 in modern English
22
Scrabble Score
14
Letters
4
Syllables
10
Unique Chars
Meaning
noun
A ring (which is also a commutative algebra), denoted K[X], formed from the set of polynomials (usually of one variable, in a given set, X), with coefficients in a given ring (often a field), K.
Example Sentences
- "It then follows that if A is a graded ring over a local ring, A is a homomorphic image of a polynomial ring over a regular local ring. For the sake of brevity, we refer to a graded polynomial ring over a regular local ring simply as a graded polynomial ring."
- "In Section 3.2 we shall study the special properties of a polynomial ring over a field; for the moment we note a property of polynomial rings which applies quite generally, the Hilbert basis theorem (after David Hilbert, 1862-1943): Theorem 3.3 If R is any right Noetherian ring, the polynomial ring R#91;x#93; is again right Noetherian."
- "Because they possess a rich theory and provide an excellent source of examples and counterexamples, integer-valued polynomial rings have attained some prominence in the theory of non-Noetherian commutative rings."
Inflected Forms
Phrases
skew polynomial ring
ring of formal power series
ring of polynomial functions
ring of regular functions
Frequently Paired Words
ring of formal power series
ring of polynomial functions
ring of regular functions