Noun
polynomial ring (plural polynomial rings)
(algebra) 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: let f be a polynomial in one variable; i.e., an element in a polynomial ring R. Then is an element in and is divisible by h in that ring. Source: Internet
By iteration, a polynomial ring in any number of variables over any UFD (and in particular over a field) is a UFD. Source: Internet
In particular, many local problems in algebraic geometry may be attacked through the study of the generators of an ideal in a polynomial ring. Source: Internet
It is called the polynomial ring over R. More generally, the set of all polynomials in variables forms a commutative ring, containing as subrings. Source: Internet
It turns out that an algebraic set is a variety if and only if it may be defined as the vanishing set of a prime ideal of the polynomial ring. Source: Internet
Note a formal power series ring does not have the universal property of a polynomial ring; a series may not converge after a substitution. Source: Internet