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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.
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. …
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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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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 …
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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