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Show that $\operatorname{rad}(I)=\bigcap P$ for all $P$ prime containing $I$

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#abstract-algebra #ring-theory #ideals #maximal-and-prime-ideals
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Intuition in studying splitting and ramification of prime ideals

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#number-theory #algebraic-number-theory #maximal-and-prime-ideals #ramification
368
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Morita equivalent rings have homeomorphic spectra?

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#abstract-algebra #ring-theory #maximal-and-prime-ideals
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Maximal ideals of $\Bbb R[x,y]/(x^2+1,y^2-1)$

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#maximal-and-prime-ideals
253
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Example of splitting of prime ideals

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#algebraic-number-theory #cyclotomic-polynomials #maximal-and-prime-ideals #ramification
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maximal ideal of matrix ring

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#ring-theory #maximal-and-prime-ideals
530
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Isomorphism of Localization of $A_\mathfrak{p}$ and $A_\mathfrak{q}$

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#abstract-algebra #commutative-algebra #maximal-and-prime-ideals #localization
56
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$R/\langle p \rangle$ is an integral domain, proof verification

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#abstract-algebra #ring-theory #solution-verification #maximal-and-prime-ideals
81
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Grade of a maximal ideal in a polynomial ring

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#commutative-algebra #maximal-and-prime-ideals
125
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Density of integers that are norms of ideals for $K \ne \mathbb{Q}$

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#algebraic-number-theory #ideals #prime-factorization #maximal-and-prime-ideals
29
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Solution of an equation in quotient-group?

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#polynomials #ideals #maximal-and-prime-ideals
131
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on the infinite power of the maximal ideal

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#ring-theory #commutative-algebra #maximal-and-prime-ideals #germs
107
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Two decomposition groups. Are they the same?

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#algebraic-number-theory #maximal-and-prime-ideals #ramification
60
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An extension $w$ of a valuation $v$ induced from $\mathfrak{p}$ come from ideal $\mathfrak{q}$ above $\mathfrak{p}$?

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#number-theory #algebraic-number-theory #valuation-theory #maximal-and-prime-ideals
33
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$\mathfrak{ap\subsetneq a}$ , with $\mathfrak{a,p}$ ideals

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#ideals #maximal-and-prime-ideals #domain-theory

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