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I am not so familiar with the theory of measures which Andre Weil uses to develope the Class Field Theory.
However, I am interested in learning algebraic number theory and I recently found that the basic ideas of commutative algebra are not so familiar with me:).
Besides, the fundamental notion of algebraic number theory in Neukirch's book Algebraic number theory is the Minkowski Theory which is quite unclear to me.
Is there any book except for those of Bourbaki on the topic of commutative algebra and Minkowski theory such that it is friendly to beginners?
Thank you very much.

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By Minkowski Theory, do you mean geometry of numbers / convex body theorem stuff, or something else? –  Pete L. Clark Feb 9 '11 at 15:11
    
Yes, it is exactly that what you mean. –  awllower Feb 10 '11 at 1:15
    
Although there is another subject also called geometry of numbers and is essentially different from Minkowski Theory which is why I took this name following Neukirch. –  awllower Feb 10 '11 at 1:19
    
Weil worked on conformal field theory?? I never knew! (I kid. But seriously: down with unexplained abbreviations!) –  Tom Leinster Feb 10 '11 at 9:02
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You use the abbreviation "CFT", which among other things could stand for Conformal Field Theory or Class Field Theory. ("Field" means different things in the two contexts, for what it's worth.) I assume you mean class field theory. I was trying to point out, gently, that using abbreviations like this without defining them is almost never a good idea. The time it takes you to type it out in full will save many other people from having to spend time figuring out what you mean. It's a courtesy, in other words. –  Tom Leinster Feb 10 '11 at 14:46

1 Answer 1

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You might try Pierre Samuel, "Algebraic Number Theory", for a concise introduction with basic treatments of what you are asking about.

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Thanks, I will try. –  awllower Feb 10 '11 at 1:15
    
Well, then what about the book Commutative Algebra by Pierre Samuel? –  awllower Feb 11 '11 at 3:38
    
If you mean Zariski-Samuel, it is oriented towards the needs of algebraic geometers. –  Charles Matthews Feb 11 '11 at 7:02
    
Thanks for answering my question. –  awllower Feb 11 '11 at 8:49
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Re: Zariski and Samuel: it is two volumes. The first volume remains one of the more graceful, lucid takes on commutative algebra. It is the second volume which tackles more specialized material in the service of (not exactly au courant but still of some interest) algebraic geometry. So it was quite maddening to me when I recently tried to order both volumes and found that the first volume (only) was out of print. It's this kind of thing that makes me want to kiss all publishers (where of course I don't mean kiss, but I don't really mean the other word either so I won't write it). –  Pete L. Clark Feb 11 '11 at 13:22

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