On prime ideals and radicals of polynomial rings and graded rings

2014 ◽  
Vol 218 (2) ◽  
pp. 323-332 ◽  
Author(s):  
P.-H. Lee ◽  
E.R. Puczyłowski
Keyword(s):  
Polynomial Rings ◽  
Prime Ideals ◽  
Graded Rings

Poisson Prime Ideals of Poisson Polynomial Rings

2007 ◽  
Vol 35 (10) ◽  
pp. 3007-3012 ◽  
Author(s):  
Sei-Qwon Oh
Keyword(s):  
Polynomial Rings ◽  
Prime Ideals

scholarly journals Prime Ideals Lying over Zero in Polynomial Rings

1995 ◽  
Vol 175 (1) ◽  
pp. 188-198 ◽  
Author(s):  
C Shah
Keyword(s):  
Polynomial Rings ◽  
Prime Ideals

On isomorphic polynomial rings over graded rings

1984 ◽  
Vol 43 (5) ◽  
pp. 418-421
Author(s):  
Yasunori Ishibashi
Keyword(s):  
Polynomial Rings ◽  
Graded Rings

scholarly journals PRESENTATIONS AND MODULE BASES OF INTEGER-VALUED POLYNOMIAL RINGS

2012 ◽  
Vol 12 (01) ◽  
pp. 1250137 ◽  
Author(s):  
JESSE ELLIOTT
Keyword(s):  
Class Group ◽  
Polynomial Rings ◽  
Prime Ideals ◽  
Closure Operation ◽  
Quotient Field ◽  
Generators And Relations ◽  
Unique Factorization Domain ◽  
Krull Domain ◽  
Finite Norm

Let D be an integral domain with quotient field K. For any set X, the ring Int (DX) of integer-valued polynomials onDX is the set of all polynomials f ∈ K[X] such that f(DX) ⊆ D. Using the t-closure operation on fractional ideals, we find for any set X a D-algebra presentation of Int (DX) by generators and relations for a large class of domains D, including any unique factorization domain D, and more generally any Krull domain D such that Int (D) has a regular basis, that is, a D-module basis consisting of exactly one polynomial of each degree. As a corollary we find for all such domains D an intrinsic characterization of the D-algebras that are isomorphic to a quotient of Int (DX) for some set X. We also generalize the well-known result that a Krull domain D has a regular basis if and only if the Pólya–Ostrowski group of D (that is, the subgroup of the class group of D generated by the images of the factorial ideals of D) is trivial, if and only if the product of the height one prime ideals of finite norm q is principal for every q.

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