Bourbaki, Nicolas. <br/><br/>
Commutative algebra :  chapters 1-7  

 - Berlin :  Springer-Verlag,  1989. 
 - xxiv, 625 p. :  ill. ;  24 cm. 
 -  Elements of mathematics .
 - Elements of mathematics .
 - Bourbaki, Nicolas.  Elements of mathematics. .
<br/><br/> Translation of: Algebre commutative. 
<br/><br/>Includes bibliographical references (p. 603-606) and indexes. 
<br/><br/> This is the softcover reprint of the English translation of 1972 (available from Springer since 1989) of the first 7 chapters of Bourbaki's 'Algèbre commutative'. It provides a very complete treatment of commutative algebra, enabling the reader to go further and study algebraic or arithmetic geometry. The first 3 chapters treat in succession the concepts of flatness, localization and completions (in the general setting of graduations and filtrations). Chapter 4 studies associated prime ideals and the primary decomposition. Chapter 5 deals with integers, integral closures and finitely generated algebras over a field (including the Nullstellensatz). Chapter 6 studies valuation (of any rank), and the last chapter focuses on divisors (Krull, Dedekind, or factorial domains) with a final section on modules over integrally closed Noetherian domains, not usually found in textbooks. Useful exercises appear at the ends of the chapters. 
<br/><br/><label>ISBN: </label>9783540642398 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Commutative algebra.<br/>algebraic geometry<br/>arithmetical<br/>commutative algebra<br/>divisors