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Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
6
votes
"Inner product" between prime factorizations
Here is a high-brow way to interpret your construction.
Recall that the ideles $\mathbb{A}^\times$ of $\mathbb{Q}$ are defined to be the restricted direct product of $\mathbb{R}^\times$ and all $\mat …
6
votes
Accepted
Minimal fields of isomorphism for varieties
Yes if $K=\mathbb{R}$ for example, but no in general.
Namely this fails for curves of genus $1$, over $\mathbb{Q}$, say. Given an elliptic curve $E$ over $\mathbb{Q}$ and a positive integer $d$, a ge …