All Questions

I am interested in the history of the proof of Artin's Theorem (on the diassociativity of alternative rings). Question. When has Artin proved this theorem and where was it published for the first ...

Presumably it was Hilbert who discovered Hilbert polynomials - where did they first appear? The basic theorem is that for a finitely generated graded module $M = \bigoplus_k M_k$ over the ring of ...

Where was $I_x/I_x^2$ first introduced? (DG or AG) asks about the algebraic cotangent space. The paper First neighborhood of the diagonal and geometric distributions by Kock claims Grothendieck ...

Cotangent space appears in both differential geometry (DG) and algebraic geometry (AG). In DG, given a smooth manifold $M$ and $x\in M$ one has an isomorphism $I_x/I_x^2 \cong T^*_xM$, where $I_x$ is ...

It is an interesting fact that a commutative ring $R$ is noetherian if and only if direct sums of injective $R$-modules are injective, and if and only if every injective $R$-module is a direct sum of ...

Page $117$ of Atiyah, MacDonald's Introduction to Commutative Algebra text has the following theorem. Let $P(M,t)$ denote the Poincare- series of $M$. $\textbf{Theorem.}$ $\bigl(\mathsf{Hilbert-Serre}...