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

2.the number of left maximal ideals of Artinian ring maybe infnite https://math.stackexchange.com/questions/2452677/question-about-semi-local-ring-and-artin-ring

3.a story of koszul complex.
https://math.stackexchange.com/questions/159318/motivation-for-koszul-complex/41141

4.where we use the cocylce condition in Gluing sheaves.
https://math.stackexchange.com/questions/2367893/details-of-gluing-sheaves-on-a-cover

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

6.bimodule structure in Ext^i_R(M,N) when $R$ is commutative.https://math.stackexchange.com/q/3005619

7.Serre quotient.https://math.stackexchange.com/q/3247686/453628

8.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.
https://math.stackexchange.com/q/974825/453628

https://math.stackexchange.com/q/121831/453628

https://math.stackexchange.com/q/139549/453628

https://math.stackexchange.com/q/1970651/453628

https://math.stackexchange.com/questions/454320/when-are-finite-index-subgroups-of-a-lie-grou
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.

10.graded free is stronger than free https://math.stackexchange.com/q/557402/453628

11.derived categroy of P^1 and derived cat of Kronecker algebra. Why are coherent sheaves on $\Bbb P^1$ derived equivalent to representations of the Kronecker quiver?

12.If $B$ is serre subcategory of abelian category of $A$, then $D(B)\rightarrow D_B(A)$ may be not fully faithful. But this is ture for bounded(Miyachi) Equivalence between a derived subcategory and a subcategory of the derived category https://math.stackexchange.com/q/2670693/453628