Solutions to Atiyah and MacDonald’s Introduction to. Commutative Algebra. Athanasios Papaioannou. August 5, Introduction to. Commutative Algebra. M. F. ATIYAH, FRS. I. G. MACDONALD. UNIVERSITY OF OXFORD. I. ADDISON-WESLEY PUBLISHING COMPANY. Atiyah and Macdonald explain their philosophy in their introduction. Two radicals of a ring are commonly used in Commutative Algebra: the.
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On page 8, the proof of part ii of Proposition 1. I suggest the following restatement:.
reference request – Prerequisites for Atiyah Macdonald – Mathematics Stack Exchange
Cassels and Froehlich see Erratum for Cassels-Froehlich. Atiyah and Wall forgot to mention the crucial compatibility between change of groups and connecting morphisms. It seems to me that the second part of the proof of Theorem 8. Pagelines Pageproof of Proposition macdonnald It seems to me the proof of Proposition I suggest to keep the proof, but to weaken slightly the statement, the new statement being: This new statement applies to the first equality in the last display in the proof of Proposition On page 29, the example at the top has two typos: Nearly all the mistakes pointed out so far were fixed in the Russian translation, which was done by Manin.
I’ll list in parentheses the page numbers of the translation where the original error still occurs for the 5 people who might care.
The translation is usually 11 page numbers ahead of the original. Scan the answers posted before this one to determine which mistakes I am referring to. There were also completely original mistakes added especially for the translation! On page kntroduction line -7 and page 31 lines 10 and 14 of the translation, the tensor product signs should be direct sum signs. On page 32 in the statement of Nakayama’s Lemma, the ideal a should be in fraktur font.
A-M defines embedded primes znd decomposable ideals only. And it doesn’t seem that a radical ideal should automatically be decomposable.
If you take something like a reduced nonnoetherian ring with infinitely many minimal prime ideals, I expect the zero ideal will be radical but not decomposable Suppose i is false”. On page 23, in the third line of the sketch for Proposition 2. On page 65 at the end of the proof of proposition 5.
On page 66 we need to correct the proof of corollary 5. Then by the previous coommutative, 5. It is a non-zero principal ideal. On page 91, the second atiyag in the second Example should refer to Proposition 8. I originally did it as hinted However, a’ does imply the original c’. Also, there should perhaps be an entry “Ideal, irreducible, 82” in the index on p.
Here is what I found in LaTeX unlike in the original ; only two of the errors mentioned below both indicated have been reported in previous answers here. See their answer above from Feb 5, See their answer above from July 17, Proof of Theorem On Chapter 2 p.
I think this question should be community wiki. I’ve just corrected the spelling of Ian G. Macdonald’s name, to avoid confusion with the less famous group theorist Ian D. Aside from this, I think it’s pointless to use this site to assemble errata for a book.
The answer to the question about a Web source of errata is very likely no. If anybody wants to start a special Web site for this purpose, it’s fine with me.
Virtually all math books do have at least minor errors. Let me try and “refute” the “high-profile organizer” comment above.
To be frank, MO just turned out to be a atigah for the Cassels-Froehlich errata rather than anything else. The reason I got so many was not because I posted here. Comkutative was because I asked for errata in many places rather than just here, all at the same timebut, crucially, I also approached several high-profile people personally Hendrik Lenstra, Rene Schoof, J.
Serre, the Conrads [before, I think, they were MO-active] and others and asked them if they had anything to send me Note that almost all of the answers in that thread were posted by me, and are of the form “prof X just sent me this big commutaive. I really pushed to make the errata, and, because I had a deadline myself the LMS wanted to republish with the errata in I had to push the people I was asking.
I worked very hard to make those errata. So, it’s very different to just posting once here and then sitting back and hoping which, I thinkis what is happening here, although I do apologise if I’ve got this wrong.
Also C-F was typeset by a company who had very OhI should have mentioned Birch and Tate in my list of bigshots I approached directly, and I’m sure there are others I’ve forgotten.
Do you think we should create an errata here? I think we should stick to the community wiki format: This has the advantage that posts can then be commented algdbra refuted! Anyway, given my admiration for this almost perfect book, I conjecture that we will find very few errata Dear Tim, let me clarify my point of view. Shouldn’t somebody make contact with Sir Atiyah?
Honorary titles in the British system are truly mysterious, but “Sir Atiyah” is actually “Sir Michael”.
Similarly, Swinnerton-Dyer is known as “Sir Peter”. But lords and ladies are even more troublesome: Depends on birth order among other things, complicated by lifetime peerages for some.
Feel free to call me Lord Jim I suggest the following restatement: Page 29, about two third of the page: Page 39, last line: Page 63, proof of Lemma 5. I rewrote in a hopefully correct way the last edit. Dear Anna, you are exactly right. The way I saw that, either a a is decomposable, and this makes sense or b a is not decomposable, hence a fortiori has no embedded prime ideals! The bracketed text should read “Use Exercises 25 and 26”. And a semantic quibble rather than a mistake: I was confused for some time by the wording of exercise 5.
I’ve since concluded that A-M uses “homomorphism into” here to mean just “homomorphism to,” i. Oct 18 ’10 at What’s a finite subject? Well, that’s the darned thing about correcting errata — you just end up introducing new errors! Oct 25 ’10 at 2: KConrad, it is a subject that is not equisemantic with any proper subsubject. LSpice thanks for your timely response! Sorry to resurrect this thread, but this error and its absence from this list confused a friend on Math SE.
Sorry to resurrect this thread but this also confused me for a second. On page 31, the first line refers to Proposition 2. PageExercise 5, the short exact sequence is missing the middle term. On page 41 in the proof of proposition 3. SE On page 77 in the proof of proposition 6. I’m reading the edition.