To give the opposite suggestion from Bart, I was going to recommend Matsumura's Commutative ring theory as opposed to his Commutative algebra. I have said why at length on the "unanswered questions" thread asking exactly Pete's question. Briefly, Ring theory is clearer, better organized, argued more fully, with more exercises (and answers), references, with a better index, and easier to read. Probably because Miles Reid rendered it into English, and possibly also because Matsumura got to revise his first book, which was almost a set of (excellent, and advanced) class lecture notes. At least two of us who took Matsumura's class in 1967 (Sevin Recillas and I) seem to like the second book. Sevin owned and recommended it when i complained I had difficulty using the original book. Since I am judging based on what appears on Amazon, I cannot be positive it contains every result I want to reference, but from the table of contents I would guess it does. I also like Zariski and Samuel for clarity, but homological methods were introduced just as that book was finished.
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To give the opposite suggestion from Bart, I was going to recommend Matsumura's Commutative ring theory as opposed to his Commutative algebra. I have said why at length on the "unanswered questions" thread asking exactly Pete's question. Briefly, Ring theory is clearer, better organized, argued more fully, with more exercises (and answers), references, with a better index, and easier to read. Probably because Miles Reid rendered it into English, and possibly also because Matsumura got to revise his first book, which was almost a set of (excellent, and advanced) class lecture notes. At least two of us who took Matsumura's class in 1967 (Sevin Recillas and I) seem to like the second book. Sevin owned and recommended it when i complained I had difficulty using the original book. Since I am judging based on what appears on Amazon, I cannot be positive it contains every result I want to reference, but from the table of contents I would guess it does. |
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