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How do I sell out with abstract algebra?

Does $R[x] \cong S[x]$ imply $R \cong S$?

Does every Abelian group admit a ring structure?

"Cayley's theorem" for Lie algebras?

Why does $(A/I)\otimes_R (B/J)\cong(A\otimes_R B)/(I\otimes_R 1+1\otimes_R J)$?

Hom and tensor with a flat module

Does a finite ring's additive structure and the structure of its group of units determine its ring structure?

implicit equation for "double torus" (genus 2 orientable surface)

Is the localization of a PID a PID?

What are the limit points of $\tan(\mathbb{N})$ in $\mathbb{R}$?

Can any smooth manifold be realized as the zero set of some polynomials?

Variety generated by finite fields

How to compute the sum of every $k$-th binomial coefficient?

Showing that if $R$ is a commutative ring and $M$ an $R$-module, then $M \otimes_R (R/\mathfrak m) \cong M / \mathfrak m M$.

Killing successive homotopy groups via fibrations

$C \otimes A \cong C \otimes B$ does not imply $A \cong B$