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Results tagged with ac.commutative-algebra
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user 100
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
2
votes
1
answer
223
views
Are non-maximal orders in number fields Grothendieck rings?
Recall that a ring homomorphism A->B is geometrically regular if for all primes p of A, the fiber of B over p is geometrically regular over k(p). A Grothendieck ring (or, G-ring) is one for which A_p- …
- 5,062
5
votes
On a morphism from the Brauer group to the Picard group
Here is another way to see that the given map should be zero. It corresponds to a map of sheaves of grouplike $\mathbb{E}_\infty$-spaces $K(\mathbb{G}_m,2)\rightarrow K(\mathbb{G}_m,1)$. All such maps …
- 5,062
-1
votes
Can a quotient ring R/J ever be flat over R?
I believe that one can use an Eilenberg swindle-type argument. Let N denote the positive integers. Let A=Z[N] denote the Z-polynomial ring on N. Create a surjective morphism A->A by sending x_1 to zer …
- 5,062
-1
votes
Can a quotient ring R/J ever be flat over R?
Here is a better (read: correct) answer than what I tried above.
There is a ring we all known and love: the ring of dual numbers, k[e]/(e^2). I claim that k=(k[e]/(e^2))/(e) is a projective k[e]/(e^2 …
- 5,062