کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9493158 | 1334211 | 2005 | 16 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Irreducible polynomials and full elasticity in rings of integer-valued polynomials
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
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).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 293, Issue 2, 15 November 2005, Pages 595-610
Journal: Journal of Algebra - Volume 293, Issue 2, 15 November 2005, Pages 595-610
نویسندگان
Scott T. Chapman, Barbara A. McClain,