I'm no expert on the evolution of Cohen-Macaulay rings, so I will leave that part of your question for those who actually know their history.

On a high level, Cohen-Macaulay rings are wonderful precisely because they lie within the intersection of algebraic geometry, algebraic topology, combinatorics, commutative algebra, and probably another four or five active research fields which I lack the perspective to mention. As such, there are plenty of "hooks" for people with diverse backgrounds to use what they know to prove something cool in a seemingly disparate field. I haven't touched commutative algebra with a ten-foot pole in my own research, but hey: I understand link conditions on simplicial complexes, so I have something to latch on to when I read about C-M rings.

For a precise sequence of as many as 9 answers to your specific question that were relevant as early as 1978, I would recommend the introduction of this paper by Melvin Hochster. It is called "Cohen Macaulay Rings and their Modules".

I'm no expert on the evolution of Cohen-Macaulay rings, so I will leave that part of your question for those who actually know their history.

On a high level, Cohen-Macaulay rings are wonderful precisely because they lie within the intersection of algebraic geometry, algebraic topology, combinatorics, commutative algebra, and probably another four or five active research fields which I lack the perspective to mention. As such, there are plenty of "hooks" for people with diverse backgrounds to use what they know to prove something cool in a seemingly disparate field. I haven't touched commutative algebra with a ten-foot pole in my own research, but hey: I understand link conditions on simplicial complexes, so I have something to latch on to when I read about C-M rings.

For a precise sequence of as many as 9 answers to your specific question that were relevant as early as 1978, I would recommend the introduction of this paper by Melvin Hochster. It is called "Cohen Macaulay Rings and their Modules".

Update (Nov 24, 2014): A fairly comprehensive introduction to the importance of Cohen-Macaulay complexes can now also be found in Anders Björner's recent article dedicated to Richard Stanley on his 70th birthday.

I'm no expert on the evolution of Cohen-Macaulay rings, so I will leave that part of your question for those who actually know their history.

On a high level, Cohen-Macaulay rings are wonderful precisely because they lie within the intersection of algebraic geometry, algebraic topology, combinatorics, commutative algebra, and probably another four or five active research fields which I lack the perspective to mention. As such, there are plenty of "hooks" for people with diverse backgrounds to use what they know to prove something cool in a seemingly disparate field. I haven't touched commutative algebra with a ten-foot pole in my own research, but hey: I understand link conditions on simplicial complexes, so I have something to latch on to when I read about C-M rings.

For a precise sequence of as many as 9 answers to your specific question that were relevant as early as 1978, I would recommend the introduction of this paper by Melvin Hochester. It is called "Cohen Macaulay Rings and their Modules".

I'm no expert on the evolution of Cohen-Macaulay rings, so I will leave that part of your question for those who actually know their history.

On a high level, Cohen-Macaulay rings are wonderful precisely because they lie within the intersection of algebraic geometry, algebraic topology, combinatorics, commutative algebra, and probably another four or five active research fields which I lack the perspective to mention. As such, there are plenty of "hooks" for people with diverse backgrounds to use what they know to prove something cool in a seemingly disparate field. I haven't touched commutative algebra with a ten-foot pole in my own research, but hey: I understand link conditions on simplicial complexes, so I have something to latch on to when I read about C-M rings.

For a precise sequence of as many as 9 answers to your specific question that were relevant as early as 1978, I would recommend the introduction of this paper by Melvin Hochster. It is called "Cohen Macaulay Rings and their Modules".