Number Fields (Universitext) 2nd Edition by Daniel A. Marcus (PDF)

Description

Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, pedestrian manner. It therefore avoids local methods and presents proofs in a way that highlights the important parts of the arguments. Readers are assumed to be able to fill in the details, which in many places are left as exercises.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Excellent book. New typeset.

⭐This book covers all of the material you would expect to encounter in a first course about number fields, and then some more. It’s wonderfully put together and has an extremely large supply of exercises to keep you engaged with the text. Be aware that lots of things are introduced solely in the exercises, so new readers should be aware of these or they will miss out on some important ideas. It’s written in a friendly style, and the proofs are worked through well. Suitable for a bright undergraduate with some good algebra experience, including Galois theory if you want to tackle the second half of the book.The content is roughly as follows:The first three chapters cover the basic properties of number fields, working up to a unique factorisation theorem for number rings modelled on the integers. You know that the integers have unique factorisation, and may have seen that the Gaussian integers have unique factorisation, but in general we need to talk about ideals to recover the analogous theorem. Chapter 4 requires some Galois theory, and shows how this theory interacts with the study of number fields, then Chapter 5 introduces the ‘geometry of numbers’ and uses it to give a complete description of the units of a number ring. The final chapters talk about some extra topics, for example zeta functions and an introduction to class field theory, which have applications to the distribution of primes.

⭐Nivel superior. Completo. De referencia. Pero exige bastante conocimientos previos. Los ejercicios no están resueltosIt’s a very nice read.

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