{"product_id":"the-decomposition-of-primes-in-torsion-point-fields-paperback","title":"The Decomposition of Primes in Torsion Point Fields - Paperback","description":"\u003cp\u003eby \u003cb\u003eClemens Adelmann\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003eIt is an historical goal of algebraic number theory to relate all algebraic extensionsofanumber?eldinauniquewaytostructuresthatareexclusively described in terms of the base ?eld. Suitable structures are the prime ideals of the ring of integers of the considered number ?eld. By examining the behaviouroftheprimeidealswhenembeddedintheextension?eld, su?cient information should be collected to distinguish the given extension from all other possible extension ?elds. The ring of integers O of an algebraic number ?eld k is a Dedekind ring. k Any non-zero ideal in O possesses therefore a decomposition into a product k of prime ideals in O which is unique up to permutations of the factors. This k decomposition generalizes the prime factor decomposition of numbers in Z Z. In order to keep the uniqueness of the factors, view has to be changed from elements of O to ideals of O . k k Given an extension K\/k of algebraic number ?elds and a prime ideal p of O, the decomposition law of K\/k describes the product decomposition of k the ideal generated by p in O and names its characteristic quantities, i. e. K the number of di?erent prime ideal factors, their respective inertial degrees, and their respective rami?cation indices. Whenlookingatdecompositionlaws, weshouldinitiallyrestrictourselves to Galois extensions. This special case already o?ers quite a few di?culties\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 148\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.34 x 9.21 x 6.14 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e May 22, 2001\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":42105765658759,"sku":"9783540420354","price":80.93,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0601\/2623\/2711\/files\/d50acd8b77a213dd451df3663847b983.webp?v=1732437587","url":"https:\/\/booksby.splitshops.com\/products\/the-decomposition-of-primes-in-torsion-point-fields-paperback","provider":"Books by splitShops","version":"1.0","type":"link"}