From the blog
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Let R be a local ring and a,b in R such that (a)=(b). Prove that there exists a unit r of R such that a=rb.
We have a=rb and b=sa for some element r and s of R. Then a=rsa so a(1-rs)=0. Clearly if a=0 then b=0 and we can…
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If f∈ℤ[x,y] generete only prime, then f is constant.
Suppose f is not constant, then, since ℤ[x,y]=(ℤ[y])[x] we can write: f=a+f₁(y)x + … + fk(y)xᵏ where fi ∈ ℤ[y] and fi≠0 for every i=1,…,k.…
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Is it true that any closed set of an arbitrary topological space X is the boundary of some subset of X?
In general this question has a negative answer: take a discrete topological space X and Z a non empty closed subset of X. Suppose Z=Fr(A)…
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Let F be a field. Can F be realized as a quotient of ℤ[i] ?
Lemma 1: If F ≅ ℤ[i]/J for some ideal J of ℤ[i] then F is a finite field. Proof: It is sufficient to show that…
Marco Damele 