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Results tagged with ac.commutative-algebra
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user 2024
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
27
votes
5
answers
3k
views
Class number measuring the failure of unique factorization
The statement that the class number measures the failure of the ring of integers to be a ufd is very common in books. ufd iff class number is 1. This inspires the following question:
Is there a quant …
- 4,593
3
votes
Accepted
Infinite collection of elements of a number field with very similar annihilating polynomials
For $n>4$, almost all fields of degree $n$ will have $r>1$:
Fix a field $K$ with discriminant $D_0$. Fix the $n-1$ coefficients $b_{n-1},...,b_{i+1}, b_{i-1},..., b_0$. The discriminant of the polyno …
- 4,593