Download or read book Integer valued Polynomials written by Paul-Jean Cahen and published by American Mathematical Soc.. This book was released on 1997 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integer-valued polynomials on the ring of integers have been known for a long time and have been used in calculus. Polya and Ostrowski generalized this notion to rings of integers of number fields. More generally still, one may consider a domain $D$ and the polynomials (with coefficients in its quotient field) mapping $D$ into itself. They form a $D$-algebra - that is, a $D$-module with a ring structure. Appearing in a very natural fashion, this ring possesses quite a rich structure, and the very numerous questions it raises allow a thorough exploration of commutative algebra. Here is the first book devoted entirely to this topic. This book features: thorough reviews of many published works; self-contained text with complete proofs; and numerous exercises.
Download or read book Integer valued Polynomials written by Sanjai K. Gupta and published by . This book was released on 1999 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The INTEGER VALUED POLYNOMIALS ON LUCAS NUMBERS written by Amitabh Kumer Halder and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integer-valued polynomial on a subset, S, of the set of integers, Z, is a polynomial f(x) 2 Q[x] such that f(S) Z. The collection, Int(S;Z), of such integer-valued polynomials forms a ring with many interesting properties. The concept of p-ordering and the associated p-sequence due to Bhargava [2] is used for nding integer-valued polynomials on any subset, S, of Z. In this thesis, we concentrate on extending the work of Keith Johnson and Kira Scheibelhut [14] for the case S = L, the Lucas numbers, where they work on integervalued polynomials on S = F, Fibonacci numbers. We also study integer-valued polynomials on the general 3 term recursion sequence, G, of integers for a given pair of initial values with some interesting properties. The results are well-agreed with those of [14].
Download or read book Integer valued Polynomials written by Todor Petkov Kitchev and published by . This book was released on 2010 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Integer Valued Polynomials in Algebraic Number Theory written by Hantsje Zantema and published by . This book was released on 1983 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Integer valued Polynomials and the QR property written by Reeve Mac Arthur Garrett and published by . This book was released on 2013 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Polynomials that are Integer Valued on the Fibonacci Numbers written by Kira Scheibelhut and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Integer valued Polynomials Over Quaternion Rings written by Nicholas J. Werner and published by . This book was released on 2010 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: When D is an integral domain with field of fractions K, the ring Int(D) of integer-valued polynomials over D is defined to be the set of all polynomials f(a) in K[x] such that f(a) is in D for all a in D. The goal of this dissertation is to extend the integer-valued polynomial construction to certain noncommutative rings. Specifically, for any ring R, we define the R-algebra RQ to be the set of elements of the form a + bi + cj + dk, where i, j, and k are the standard quaternion units satisfying the relations i^2 = j^2 = -1 and ij = k = -ji. When this is done with the integers Z, we obtain a noncommutative ring ZQ; when this is done with the rational numbers Q, we get a division ring QQ. Our main focus is on the construction and study of Int(ZQ), the set of integer-valued polynomials over ZQ. We also consider Int(R), where R is an overring of ZQ in QQ. In this treatise, we prove that for such an R, Int(R) has a ring structure and investigate elements, generating sets, and prime ideals of Int(R). The final chapter examines the idea of integer-valued polynomials on subsets of ZQ.
Download or read book Polynomials that are Integer Valued on the Image of an Integer valued Polynomial written by Mario V. Marshall and published by . This book was released on 2009 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let D be an integral domain and f a polynomial that is integer-valued on D. We prove that Int(f(D);D) has the Skolem Property and give a description of its spectrum. For certain discrete valuation domains we give a basis for the ring of integer-valued even polynomials. For these discrete valuation domains, we also give a series expansion of continuous integer-valued functions.
Download or read book Commutative Algebra written by Marco Fontana and published by Springer. This book was released on 2014-07-15 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a multi-dimensional collection of articles highlighting recent developments in commutative algebra. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics and research methods include Noetherian and non- Noetherian ring theory as well as integer-valued polynomials and functions. Specific topics include: · Homological dimensions of Prüfer-like rings · Quasi complete rings · Total graphs of rings · Properties of prime ideals over various rings · Bases for integer-valued polynomials · Boolean subrings · The portable property of domains · Probabilistic topics in Intn(D) · Closure operations in Zariski-Riemann spaces of valuation domains · Stability of domains · Non-Noetherian grade · Homotopy in integer-valued polynomials · Localizations of global properties of rings · Topics in integral closure · Monoids and submonoids of domains The book includes twenty articles written by many of the most prominent researchers in the field. Most contributions are authored by attendees of the conference in commutative algebra held at the Graz University of Technology in December 2012. There is also a small collection of invited articles authored by those who did not attend the conference. Following the model of the Graz conference, the volume contains a number of comprehensive survey articles along with related research articles featuring recent results that have not yet been published elsewhere.
Download or read book Integer valued Polynomials and Their Derivatives written by Angkana Sripayap and published by . This book was released on 2001 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Integer Valued Polynomials Over a Number Field written by H. Zantema and published by . This book was released on 1982 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ideals in Rings of Integer Valued Polynomials written by Demetrios Brizolis and published by . This book was released on 1973 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Commutative Algebra and Its Applications written by Marco Fontana and published by Walter de Gruyter. This book was released on 2009 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains selected refereed papers based on lectures presented at the 'Fifth International Fez Conference on Commutative Algebra and Applications' that was held in Fez, Morocco in June 2008. The volume represents new trends and areas of classical research within the field, with contributions from many different countries. In addition, the volume has as a special focus the research and influence of Alain Bouvier on commutative algebra over the past thirty years.
Download or read book Polynomials written by and published by Springer Science & Business Media. This book was released on 2009 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Homogeneous Integer valued Polynomials in Two Variables written by Donald Patterson and published by . This book was released on 2010 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Integer valued Polynomials and Pullbacks of Arithmetical Rings written by Jason Boynton and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
