# Tagged Questions

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Can anyone explain to me what $C[x^2,x^3]_{(x^2,x^3)}$ means? It is connected with localizations but it is unclear to me what it means exactly.
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### Atiyah-MacDonald 5.10

The problem says: Let $f:A\rightarrow B$ be a ring homomorphism and let $f^{*}:\operatorname{Spec}(B)\rightarrow \operatorname{Spec}(A)$ be the mapping associated with $f$. And then comes the ...
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### Show that a local ring is equicharacteristic iff it contains a subfield

A local ring $(A,\mathfrak m)$ is equicharacteristic if $\operatorname{char} A=\operatorname{char} \kappa (m)$. Need hints to solve the following question: A local ring is equicharacteristic ...
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### What does $R_P$ mean, for a ring $R$ and an ideal $P$?

What does $R_P$ mean, for a ring $R$ and an ideal $P$? This appeared in some notes by a teacher of mine, but he didn't define this notation. He used it as follows: suppose $R$ is a commutative ring, ...
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### What letter should I use to denote an ideal?

In commutative algebra, there seem to be two rather different notational conventions for ideals: either $I,J, \dots$ or $\mathfrak{a}, \mathfrak{b}, \dots$. By itself, it is hardly surprising - after ...
I've always wondered why finitely generated modules are of form $$M=Ra_1+\dots+Ra_n$$ while finitely generated algebras have form $$R=k[a_1,\dots, a_n]$$ and finite algebras have form ...