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Non-commutative rings and algebras, non-associative algebras. Can be used in combination with ra.rings-and-algebras

12 votes
1 answer
1k views

A problem in commutative algebra whose solution requires algebraic geometry (resp., noncommu...

One can argue that commutative algebra is affine algebraic geometry. However, a great deal of commutative algebra generalizes to non-commutative algebra, and in that setting there is little geometry, …
Jesse Elliott's user avatar
5 votes

Algebraic theorems with no known algebraic proofs

Dirichlet's theorem on primes in arithmetic progression: if $a$ and $b$ are any relatively prime positive integers, then there are infinitely many prime numbers of the form $a+nb$ for positive integer …