# Commutative Algebra

## List of commutative algebra topics

Abstract These notes prove the basic theorems in commutative algebra required for algebraic number theory, algebraic geometry, and algebraic groups. They assume only a knowledge of the algebra usually taught in advanced undergraduate or first-year graduate courses. Contents Rings and algebras Ideals Noetherian rings Unique factorization Rings of fractions Integral dependence The going-up and going-down theorems Noether's normalization theorem Direct and inverse limits Tensor products Flatness Finitely generated projective modules Zariski's lemma and the Hilbert Nullstellsatz The spectrum of a ring Jacobson rings and max spectra Artinian rings Quasi-finite algebras and Zariski's main theorem Dimension theory for finitely generated k -algebras Primary decompositions Dedekind domains Dimension theory for noetherian rings Regular local rings Flatness and fibres Completions History v1.

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First version on the web. Revised and completed.

## Progress in Commutative Algebra 1 : Combinatorics and Homology

Many improvements to the exposition thanks to Shu Otsuka. Added section on finitely generated projective modules; minor fixes. This little book seems to be specially suited to those who want to learn AG. It's a bit too brisk, specially at the beginning - if you don't already have an acquaintance with the basics of groups, rings and ideals, you may run into trouble - but very illuminating.

Masterful choice of topics, great exercises as a matter of fact, about half the topics of the book, and more specifically the ones that are directly related to AG, are treated in the exercises, some of them quite challenging - like one said before, it looks like a "chapter 0" of Hartshorne's book on AG.

### with a View Toward Algebraic Geometry

The authors consciously estabilish relations between the Commutative Algebra: Chapters In Stock. Not true. I think this is considered to be one of the "good" Bourbaki books. Anyway, if you "do algebra", you will probably find this book worth having eventually. The font is fine, perhaps a point small for my taste, and the printing is clear, not like those hack photocopy jobs that some of the publishers use for old books I'm looking at you Addison-Wesley. The material in this book is not usually considered "undergraduate": Noether normalization, spectra of rings, discrete valuation rings, and more.

But this book makes them very clear. If you go on in the subject you will certainly need Eisenbud's book. This is a very good starter, and a good companion to Eisenbud if you are learning the material on your own. Commutative Algebra: An Introduction. William Hoffman. Only 3 left in stock more on the way. Very nice treatment of the fundamental aspects of Commutative Algebra in a simple and direct manner.

Fantastic book, terse but lucid.

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Basic commutative algebra. Lee D.

## MA3G6 Commutative Algebra

I don't have the second edition of this book but did read the first, and the authors do a fine job of introducing the reader to the computational side of algebraic geometry. I will forego a chapter by chapter review therefore, but no doubt the second edition which I do not own is as well-written as the first. I would recommend it to anyone interested in the many applications of algebraic geometry and to those who need to understand how to compute things in algebraic geometry.

The good thing about this book is that it gives a concrete flavor to a highly abstract subject.

see url Algebraic geometry, through its applications to coding theory, cryptography, and computer graphics, is fast becoming the subject to learn. It is no longer just an esoteric, high-brow subject but one that is taking on major importance in the information age. Even without applications though it is Available for download now.

Fu USA. A great transition from elementary to advanced comm.

The proofs are clear and concise and the text is well-organized. Graduate Algebra: Commutative View.

Only 1 left in stock more on the way. Kawasaki, Kanagawa Japan.