Sign up to join this community. Appendix to 7 Pure submodules. More than one of Matsumura's former students from his course at Brandeis which gave rise to the first book, including me, themselves prefer the second one. Your title says nothing substantive, the text of your links says nothing substantive. Sign up using Email and Password. By using our site, you acknowledge that you have read and understand our Cookie Policy , Privacy Policy , and our Terms of Service. Active 5 years, 7 months ago.
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Ring Theory you will learn why he wrote the second book. By comparing the tables of contents, the two books seem to contain almost the same material, with similar organization, with perhaps the omission of the chapter on excellent rings from the first, but the second book is considerably more user friendly for learners. Your title says nothing substantive, the text of your links says nothing substantive. More advanced topics such as Ratliff's theorems on chains of prime ideals are also explored.
Matsumura covers the basic material, including dimension theory, depth, Cohen-Macaulay rings, Gorenstein rings, Krull rings and valuation rings. There dommutative two books by Matsumura on commutative algebra. Tensor products direct and inverse limits. The freeness of any projective modules over a local ring is stated in book one, proved in the finite case, and proved in general mahsumura book two.
In addition to being an interesting and profound subject in its own right, commutative ring theory is important as a foundation for algebraic geometry and complex analytical geometry.
books - Matsumura: "Commutative Algebra" versus "Commutative Ring Theory" - MathOverflow
I am a beginner in more advanced algebra and my question is very simple, I would like to know the difference between these books of the same author, Hideyuki Matsumura. Unicorn Meta Zoo 9: Mathematics Stack Exchange works best with JavaScript enabled. Incidentally, I was at first confused in reading your comment since this statement is in the introduction, not the preface, which is about why Matsumura felt it necessary to produce a second edition of the same book.
Numerous definitions and basic ring theoretic concepts were taken for granted that are defined and discussed in the second. Basically, my question is Why are there two books, by the same author, apparently on the same subject? The more recent version is called Commutative Ring Theory and is still in print. Neither entirely subsumes the other, but the 2nd covers "more" stuff. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.
Sign up using Facebook. The best answers are voted up and rise to the top. A more practical question is whether both books are equally appropriate as references when reading a book like Hartshorne.
What do you want to do in September for MO's tenth anniversary? Active 2 years, 10 months ago. He was replacing another author who, well, read the preface. Selected pages Title Page. Properties of extension rings. Derived functors such as Ext and Tor are assumed in the first book, while there is an appendix reviewing them in the second. Matsumura Cambridge University PressMay 25, - Mathematics - pages 0 Reviews In addition to being an interesting and profound subject in its own right, commutative ring theory is important as a foundation for algebraic geometry and complex analytical geometry.
MathOverflow works best with JavaScript enabled. Commutative Algebra Mathematics lecture note series ; Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. More than one of Matsumura's former students from his course at Brandeis which gave rise to the first book, including me, themselves prefer the second one.
Sign up or log in Sign up using Google. Appendix to 7 Pure submodules. However, I am curious to know the answer to the broader question as well.
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