For the past couple of years I've been currently writing what amounts to a book on commutative algebra:

http://alpha.math.uga.edu/~pete/integral2015.pdf

I say this not because I think that if/when I'm finished, my "book" will be the book you're looking for. Really! Rather, my point is that when I started writing my book I was in your situation: I had picked up "enough" commutative algebra for my research but hadn't studied it systematically since I was an undergraduate taking a 10 week course at the Atiyah-MacDonald level. There were a handful of texts that I owned and got useful information out of -- especially, Eisenbud and Matsumura -- but none of the texts covered everything that I wanted or only things that I wanted. (Also, and I don't know whether you are in this situation, I had begun to teach graduate courses and wanted to use facts of commutative algebra in my lectures. It doesn't really fly to say, "This holds by some normalization theorem, which is surely somewhere in Matsumura, or if not then in Eisenbud -- I think." They'll believe you, but they won't look it up themselves.) So...

Anyway, returning to the present, I really like my book. I especially like that I can add to it at any time I like, that I can move the sections around if I choose to, that I have free access to it at all times, etc. There is no doubt in my mind that in writing it I have learned an immense amount of material. In particular, I have long since disabused myself of the somewhat jejeune notion that I knew "enough" commutative algebra. I no longer believe that such a thing is even possible.

This is not to say that no one else cares about my "great 21st century commutative algebra book". I have gotten a lot of feedback to the contrary, and I do think it -- or rather, parts of it -- are being read by a worldwide audience. Conversely, I regularly peruse other people's great 21st century commutative algebra books for nuggets of insight. I look forward to reading yours...

For the past couple of years I've been currently writing what amounts to a book on commutative algebra:

http://alpha.math.uga.edu/~pete/integral2015.pdf

I say this not because I think that if/when I'm finished, my "book" will be the book you're looking for. Really! Rather, my point is that when I started writing my book I was in your situation: I had picked up "enough" commutative algebra for my research but hadn't studied it systematically since I was an undergraduate taking a 10 week course at the Atiyah-MacDonald level. There were a handful of texts that I owned and got useful information out of — especially, Eisenbud and Matsumura — but none of the texts covered everything that I wanted or only things that I wanted. (Also, and I don't know whether you are in this situation, I had begun to teach graduate courses and wanted to use facts of commutative algebra in my lectures. It doesn't really fly to say, "This holds by some normalization theorem, which is surely somewhere in Matsumura, or if not then in Eisenbud — I think." They'll believe you, but they won't look it up themselves.) So ….

Anyway, returning to the present, I really like my book. I especially like that I can add to it at any time I like, that I can move the sections around if I choose to, that I have free access to it at all times, etc. There is no doubt in my mind that in writing it I have learned an immense amount of material. In particular, I have long since disabused myself of the somewhat jejune notion that I knew "enough" commutative algebra. I no longer believe that such a thing is even possible.

This is not to say that no one else cares about my "great 21st century commutative algebra book". I have gotten a lot of feedback to the contrary, and I do think it — or rather, parts of it — are being read by a worldwide audience. Conversely, I regularly peruse other people's great 21st century commutative algebra books for nuggets of insight. I look forward to reading yours….

Dear Andrea,

For the past couple of years I've been currently writing what amounts to a book on commutative algebra:

http://www.math.uga.edu/~pete/integral.pdf

I say this not because I think that if/when I'm finished, my "book" will be the book you're looking for. Really! Rather, my point is that when I started writing my book I was in your situation: I had picked up "enough" commutative algebra for my research but hadn't studied it systematically since I was an undergraduate taking a 10 week course at the Atiyah-MacDonald level. There were a handful of texts that I owned and got useful information out of -- especially, Eisenbud and Matsumura -- but none of the texts covered everything that I wanted or only things that I wanted. (Also, and I don't know whether you are in this situation, I had begun to teach graduate courses and wanted to use facts of commutative algebra in my lectures. It doesn't really fly to say, "This holds by some normalization theorem, which is surely somewhere in Matsumura, or if not then in Eisenbud -- I think." They'll believe you, but they won't look it up themselves.) So...

Anyway, returning to the present, I really like my book. I especially like that I can add to it at any time I like, that I can move the sections around if I choose to, that I have free access to it at all times, etc. There is no doubt in my mind that in writing it I have learned an immense amount of material. In particular, I have long since disabused myself of the somewhat jejeune notion that I knew "enough" commutative algebra. I no longer believe that such a thing is even possible.

This is not to say that no one else cares about my "great 21st century commutative algebra book". I have gotten a lot of feedback to the contrary, and I do think it -- or rather, parts of it -- are being read by a worldwide audience. Conversely, I regularly peruse other people's great 21st century commutative algebra books for nuggets of insight. I look forward to reading yours...

For the past couple of years I've been currently writing what amounts to a book on commutative algebra:

http://alpha.math.uga.edu/~pete/integral2015.pdf

I say this not because I think that if/when I'm finished, my "book" will be the book you're looking for. Really! Rather, my point is that when I started writing my book I was in your situation: I had picked up "enough" commutative algebra for my research but hadn't studied it systematically since I was an undergraduate taking a 10 week course at the Atiyah-MacDonald level. There were a handful of texts that I owned and got useful information out of -- especially, Eisenbud and Matsumura -- but none of the texts covered everything that I wanted or only things that I wanted. (Also, and I don't know whether you are in this situation, I had begun to teach graduate courses and wanted to use facts of commutative algebra in my lectures. It doesn't really fly to say, "This holds by some normalization theorem, which is surely somewhere in Matsumura, or if not then in Eisenbud -- I think." They'll believe you, but they won't look it up themselves.) So...

Anyway, returning to the present, I really like my book. I especially like that I can add to it at any time I like, that I can move the sections around if I choose to, that I have free access to it at all times, etc. There is no doubt in my mind that in writing it I have learned an immense amount of material. In particular, I have long since disabused myself of the somewhat jejeune notion that I knew "enough" commutative algebra. I no longer believe that such a thing is even possible.

This is not to say that no one else cares about my "great 21st century commutative algebra book". I have gotten a lot of feedback to the contrary, and I do think it -- or rather, parts of it -- are being read by a worldwide audience. Conversely, I regularly peruse other people's great 21st century commutative algebra books for nuggets of insight. I look forward to reading yours...