12h
comment Hartshorne Exercise II.2.18(d)
@Manos No. $\mathfrak p$ is a point in $\Spec A$. Think of $B$ as an $A$-algebra, and localize it at the prime ideal $\mathfrak p$ of $A$. This is a valid operation that gives us the homomorphism $\varphi_\mathfrak p$. Remember that $f^\#$ is a morphism of sheaves on $\Spec A$. This is why we consider points in $\Spec A$.
12h
comment Hartshorne Exercise II.2.18(d)
@Manos If we consider $B$ as an $A$-algebra via $\varphi$, then the notation $B_\mathfrak p$ makes sense.
12h
reviewed Approve suggested edit on Let $f$ be injective and discontinuous at some point $c$. Can its inverse be continuous?
13h
answered Hartshorne Exercise II.2.18(d)
13h
comment Hartshorne Exercise II.2.18(d)
(2) is indeed superfluous. I haven't checked your proof, but note that the result quickly follows from the fact that being surjective is a local property of morphisms of sheaves and homomorphisms of algebras.
1d
comment Is torus w. disc removed homotopic to klein bottle w. disc removed?
Are you familiar with the fundamental polygons of those spaces? This should enable you to prove that both spaces are homeomorphic to a wedge sum of two circles.
1d
comment If $f : M\otimes_A A/m \to N\otimes_A A/m$ is surjective , so is $f : M \to N$.
Use the canonical isomorphism $N \otimes_A A / \mathfrak m \cong N / \mathfrak m N$.
Feb
5
comment Pick out a polynomial such that ideal $J=q(x)R$ , where $q(x)$ is polynomial and $R$ is ring
Where does this question come from? Did you learn about any of: Euclidean algorithm, GCD, PID?
Feb
3
answered If $\phi ^{-1}(X)$ is irreducible, and $X$ is contained in the image of $\phi$, show that $X$ is irreducible.
Feb
2
awarded Great Answer
Feb
1
awarded Good Answer
Dec
29
awarded Enlightened
Dec
29
awarded Nice Answer
Dec
24
comment Nonsplit extension of $\mathbb{Z}$ by itself
Are you familiar with projective modules? $\mathbb Z$ is a free $\mathbb Z$-module. Thus, every short exact sequence ending in $\mathbb Z$ splits.
Dec
9
awarded Yearling
Dec
9
awarded Yearling
Dec
1
awarded Enlightened
Dec
1
awarded Nice Answer
Nov
26
comment Limit of $L_p$ norm as $ p \rightarrow 0$
@dreammonger Would you be interested in editing my proof and adding this correction? I'd be delighted to accept it. Thanks!
Nov
23
awarded Yearling
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