Algebraic Number Theory for Beginners Stillwell John
Algebraic Number Theory for Beginners Stillwell John This book introduces algebraic number theory through the problem of generalizing 'unique prime factorization' from ordinary integers to more…
Specifikacia Algebraic Number Theory for Beginners Stillwell John
Algebraic Number Theory for Beginners Stillwell John
This book introduces algebraic number theory through the problem of generalizing 'unique prime factorization' from ordinary integers to more general domains. To restore it, we need Dedekind's concept of ideals. Solving polynomial equations in integers leads naturally to these domains, but unique prime factorization may be lost in the process.
It was left to Emmy Noether to encapsulate the properties of rings that make unique prime factorization possible, in what we now call Dedekind rings. However, one still needs the supporting concepts of algebraic number field and algebraic integer, and the supporting theory of rings, vector spaces, and modules. The book develops the theory of these concepts, following their history, motivating each conceptual step by pointing to its origins, and focusing on the goal of unique prime factorization with a minimum of distraction or prerequisites. This
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