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My answer is fairly simple, perhaps due to my own ignorance and inexperience, but since you asked: There is a non-zero risk. But the rewards for talking and sharing with people about math far outweig …

There is the Hilbert-Burch Theorem, which gives structure of Cohen-Macaulay ideals having projective dimension one in a regular or polynomial ring. The named authors published their results about 80 y …

I was reading Auslander's talk at the 1962 ICM (beginning of Section 2 on this page). At the end, the reference began: [1] M. Auslander, Modules over unramified regular local rings, Illinois. J. Math …

Recently I dug up some biographical details of Lindsay Burch, of Hilbert-Burch Theorem fame, whose few papers have had quite an impact on commutative algebra. This made me curious about the first wome …

ADDED: There is an account written by Buchsbaum (see page 1 and 2 of number 23 here) which described in more details what they wrote in [1]. So the localization problem for regular rings was definitel …

I followed the reference suggested by KConrad in the comments and found perhaps the answer to Question 1: Annie MacKinnon, who got her PhD from Cornell in 1894 with the thesis "Concomitant Binary Form …

Motivic or $A^1$-homotopy theory. Affine algebraic geometry. Cluster Algebra Portal.

First, my apology for this soft question. My excuse was that I really think this may be of interest to the community. I would understand if it gets closed (I have advocated closing some soft questions …

I am very interested in reading some and skimming through the list of invited talks at the International Congress of Mathematicians. Since the proceedings contain talks supposedly by top experts in ea …

Those of us who are old enough may remember http://www.tricki.org/ Localize + complete, taking a hypersurface section, and using the socle are useful tricks in commutative algebra.