Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9493158 | Journal of Algebra | 2005 | 16 Pages |
Abstract
Let D be a unique factorization domain and S an infinite subset of D. If f(X) is an element in the ring of integer-valued polynomials over S with respect to D (denoted Int(S,D)), then we characterize the irreducible elements of Int(S,D) in terms of the fixed-divisor of f(X). The characterization allows us to show that every nonzero rational number n/m is the leading coefficient of infinitely many irreducible polynomials in the ring Int(Z)=Int(Z,Z). Further use of the characterization leads to an analysis of the particular factorization properties of such integer-valued polynomial rings. In the case where D=Z, we are able to show that every rational number greater than 1 serves as the elasticity of some polynomial in Int(S,Z) (i.e., Int(S,Z) is fully elastic).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Scott T. Chapman, Barbara A. McClain,