Commutative Ring Theory by Matsumura: Goes deeper than Atiyah/Macdonald, but is also written quite concisely. Covers most of the material that Eisenbud does, except for the computational stuff, but has an approach that more heavily uses universal properties, whereas Eisenbud seems to favour concrete construction.
I thought these labels more represented historical trends in mathematical inquiry rather than real technical distinctions. See Difference between algebra and geometry Atiyah seems to be suggesting a distinction between the reasoning/axioms associated with geometry and those associated with algebra. Is there a difference? If so, what is it?
Atiyah-Macdonald 5.16: Geometric interpretation of Noether normalization Ask Question Asked 3 years, 2 months ago Modified 1 year, 3 months ago
I am interested in learning about Dirac operators, Heat Kernels and their role in Atiyah-Singer Index Theorem. From various sources (including this very helpful question), I have come to know of va...
Note: This is (essentially) the statement of ex 5.8 in Atiyah-Macdonald. The only extra is the fact that the degree is $\binom {n} {k}$. Found by obtaining explicit dependencies in particular cases (using Groebner bases) and noticing the degree. Posted as reference Any feedback would be appreciated!
Atiyah-McDonald Exercise 4.11 Ask Question Asked 5 years, 2 months ago Modified 5 years, 2 months ago
I have worked out a solution to exercise 2.15 of Atiyah-Macdonald, which is needed in the solution of 2.3 (see Atiyah-Macdonald 2.3). However, the solution seems overly complicated, and I am not entirely sure about the argument in part 2.
3 I don't believe this question has been asked here before, so here we go: I'm having trouble with Exercise 11.2 in Atiyah-Macdonald, which states: