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Results tagged with ac.commutative-algebra
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user 1123
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
3
votes
1
answer
259
views
Metabolic vs stably metabolic
Let $A$ be a commutative ring with unit. A non-degenerate symmetric bilinear form $\phi$ on a finitely generated projective $A$-module $P$ is called metabolic if there is a direct summand $L$ of $P$ s …
- 998
6
votes
Does every projective A/I-module come from A?
Here's an explicit counterexample:
Let $A = \mathbb{Z}$, and $I=6 \mathbb{Z}$. Then $A/I = \mathbb{Z}/6$ which is isomorphic to $\mathbb{Z}/2 \oplus \mathbb{Z}/3$ as module over itself. Since $\mathbb …
- 998