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Results tagged with ac.commutative-algebra
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user 6401
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
11
votes
Tor and projective dimension
There's another dimension, called flat dimension: $\mathrm{fd}\; M_R = n$ means that $n$ is the smallest integer such that there exists a resolution
$$0 \to F_n \to \cdots \to F_1 \to F_0 \to M \to 0$ …
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24
votes
Accepted
Does ZF prove that all PIDs are UFDs?
ZF alone does not prove that every PID is a UFD, according to this paper: Hodges, Wilfrid. Läuchli's algebraic closure of $Q$. Math. Proc. Cambridge Philos. Soc. 79 (1976), no. 2, 289--297. MR 422022. …
- 856
5
votes
Number of A Subset of Monomials
Let $S_i$ be the set of monic monomials $m \in \mathbb{Z}[x_1, \dots,
x_k]$ which are divisible by $x_i$ but not $x_i^2$. If I am reading
your question correctly, you are looking for $|S_1 \cup \cdots …
- 856
9
votes
Nilradicals without Zorn's lemma
Y. Rav proved this using the Ultrafilter Principle ("Every filter on a set can be extended to an ultrafilter"), which is weaker than the Axiom of Choice. Theorem 4.1 of Variants of Rado's selection le …
- 856