Elementary number theory is concerned with the arithmetic properties of the ring of integers, Z, and its field of fractions, the rational numbers, Q. Early on in the development of the subject it was noticed that Z has many properties in common with A = IF[T], the ring of polynomials over a finite field. Both rings are principal ideal domains, both have the property that the residue class ring of any non-zero ideal is finite, both rings have infinitely many prime elements, and both rings have finitely many units. Thus, one ...
Read More
Elementary number theory is concerned with the arithmetic properties of the ring of integers, Z, and its field of fractions, the rational numbers, Q. Early on in the development of the subject it was noticed that Z has many properties in common with A = IF[T], the ring of polynomials over a finite field. Both rings are principal ideal domains, both have the property that the residue class ring of any non-zero ideal is finite, both rings have infinitely many prime elements, and both rings have finitely many units. Thus, one is led to suspect that many results which hold for Z have analogues of the ring A. This is indeed the case. The first four chapters of this book are devoted to illustrating this by presenting, for example, analogues of the little theorems of Fermat and Euler, Wilson's theorem, quadratic (and higher) reciprocity, the prime number theorem, and Dirichlet's theorem on primes in an arithmetic progression. All these results have been known for a long time, but it is hard to locate any exposition of them outside of the original papers. Algebraic number theory arises from elementary number theory by con sidering finite algebraic extensions K of Q, which are called algebraic num ber fields, and investigating properties of the ring of algebraic integers OK C K, defined as the integral closure of Z in K.
Read Less
Add this copy of Number Theory in Function Fields: 210 (Graduate Texts to cart. $56.17, very good condition, Sold by Brit Books rated 4.0 out of 5 stars, ships from Milton Keynes, BUCKINGHAMSHIRE, UNITED KINGDOM, published 2002 by Springer.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Very good. Simply Brit – welcome to our online used book store, where affordability meets great quality. Dive into a world of captivating reads without breaking the bank. We take pride in offering a wide selection of used books, from classics to hidden gems, ensuring there's something for every literary palate. All orders are shipped within 24 hours and our lightning fast-delivery within 48 hours coupled with our prompt customer service ensures a smooth journey from ordering to delivery. Discover the joy of reading with us, your trusted source for affordable books that do not compromise on quality.
Add this copy of Number Theory in Function Fields to cart. $62.00, very good condition, Sold by Becker's Books rated 3.0 out of 5 stars, ships from Houston, TX, UNITED STATES, published 2010 by Springer.
Add this copy of Number Theory in Function Fields to cart. $70.05, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2010 by Springer-Verlag New York Inc..
Add this copy of Number Theory in Function Fields (Graduate Texts in to cart. $73.45, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2010 by Springer.
