{"product_id":"the-theory-of-algebraic-numbers-dover-books-on-mathematics-9780486404547","title":"The Theory of Algebraic Numbers (Dover Books on Mathematics)","description":"\u003cp\u003eDetailed proofs and clear-cut explanations provide an excellent introduction to the elementary components of classical algebraic number theory in this concise  well-written volume. The authors  a pair of noted mathematicians  start with a discussion of divisibility and proceed to examine Gaussian primes (their determination and role in Fermats theorem); polynomials over a field (including the Eisenstein irreducibility criterion); algebraic number fields; bases (finite extensions  conjugates and discriminants  and the cyclotomic field); and algebraic integers and integral bases. After establishing a firm introductory foundation  the text explores the uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; and the Fermat conjecture (concluding with discussions of Pythagorean triples  units in cyclotomic fields  and Kummers theorem). In addition to a helpful list of symbols and an index  a set of carefully chosen problems appears at the end of each chapter to reinforce mathematics covered. Students and teachers of undergraduate mathematics courses will find this volume a first-rate introduction to algebraic number theory.\u003c\/p\u003e","brand":"My Store","offers":[{"title":"Default Title","offer_id":45277073375285,"sku":"ByrdShop_0486404544","price":337.66,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0627\/8139\/0901\/files\/9780486404547.jpg?v=1780571501","url":"https:\/\/atxbooks.com\/products\/the-theory-of-algebraic-numbers-dover-books-on-mathematics-9780486404547","provider":"ATX Books","version":"1.0","type":"link"}