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some questions for myself.

1.https://math.stackexchange.com/questions/174595/classification-of-prime-ideals-of-mathbbzx

1. the number of left maximal ideals of Artinian ring may be infinite question about semi-local ring and Artin ring.

2. a story of the Koszul complex. Motivation for Koszul complex

3. where we use the cocycle condition in Gluing sheaves. Details of gluing sheaves on a cover

4. An intuitive approach to the Jordan Normal form.https://math.stackexchange.com/q/411845/453628

5. bimodule structure in $$\text{Ext}^i_R(M, N)$$ when $$R$$ is commutative. How do I understand the module structure on Yoneda Ext?

6. Serre quotient. Quotient of category of f.g. modules by subcategory

7. Flat vs faithfully flat.https://math.stackexchange.com/questions/394654/example-of-a-flat-but-not-faithfully-flat-ring-extension

9.GL(n,R) is not connected, GL(n,C) is connected. What's an easy way to show that $GL(n,\mathbb C)$ is connected?
Why is the determinant $M_n(\mathbb R) \to \mathbb R$ continuous?
How to show path-connectedness of $GL(n,\mathbb{C})$
How to prove $GL_n(\mathbb{C})$ has no subgroup with finite index?
When are finite-index subgroups of a Lie group closed? subgroup of a lie group with finite index is closed. Zariski topology,by GL(n,C) is open affine variety of M_n(C)=C^{n^2}. C^{n^2} is irreducible, hence GL(n,C) is irreducible and dense. Hence GL(n,C) is connected.

2. derived category of $$\text{coh}\mathbb{P}^1$$ and derived cat of Kronecker algebra. https://mathoverflow.net/q/285955/106580

3. If $$B$$ is the Serre subcategory of the abelian category of $$A$$, then $$\textbf{D}(B)\rightarrow \textbf{D}_B(A)$$ maybe not be fully faithful. But this is true for bounded(Miyachi) https://mathoverflow.net/q/236245/106580 derived category of quotient category

4. Why is an injective quasi-coherent sheaf's restriction to an open subset still an injective object? https://mathoverflow.net/q/6762/106580

5. Finite generated filed extension is finite extension(Zariski's version of Nullstellensatz)Finitely generated algebraic field extensions are finite extensions?

6. Why is the limit of $$n^{1/n}$$ is 1 How to show that $\lim_{n \to +\infty} n^{\frac{1}{n}} = 1$?

7. Radical of a ring VS radical of a module, when Rad(R)M=Rad(M)? Jacobson radical of a ring and radical of finitely generated $R$-module

8. $$\text{height}(I)+\text{dim}(R/I)=\text{dim}(R)$$ for all ideal $$I$$ of $$R$$ iff $$\text{height}(\mathfrak{p})+\text{dim}(R/\mathfrak{p})=\text{dim}(R)$$ for all prime ideal $$\mathfrak{p}$$ of $$R$$. Does codimension equal height in complete local domains?

9. Homogeneous localization and regularity

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