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$(X^m-Y^n)$ is a prime ideal in $A[X,Y]$ iff $m, n$ are coprime

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#abstract-algebra #ring-theory #commutative-algebra #irreducible-polynomials #maximal-and-prime-ideals
395
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Let π : A → A/I be the natural projection, π preserves maximals ideals.

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#abstract-algebra #ring-theory #maximal-and-prime-ideals
121
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If $f(x) \in f(p)$ then $x \in p$, for $p$ a prime ideal and $f$ a ring homomorphism

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#abstract-algebra #maximal-and-prime-ideals
216
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Decomposition of $\operatorname{Spec}A_1\times A_2$ into $\operatorname{Spec}A_1 \sqcup\operatorname{Spec}A_2$

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#abstract-algebra #ring-theory #commutative-algebra #maximal-and-prime-ideals
90
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Maximal right ideal

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#abstract-algebra #maximal-and-prime-ideals
277
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Trying to understand why the associated primes of some ideal are minimal.

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#algebraic-geometry #commutative-algebra #ideals #maximal-and-prime-ideals
282
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How do we find Associated primes Geometrically?

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#algebraic-geometry #commutative-algebra #maximal-and-prime-ideals
204
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Existence of prime ideal lying over $p \implies pS \cap R=p $?

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#commutative-algebra #maximal-and-prime-ideals
414
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$J$ maximal ideal of $A$ $\iff $ $A/J$ is field

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#abstract-algebra #ring-theory #ideals #maximal-and-prime-ideals
118
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Goldbach property for polynomials with base ring a PID with infinitely many maximal ideals

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#polynomials #ring-theory #principal-ideal-domains #noetherian #maximal-and-prime-ideals
273
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Intersection of Height One Primary Ideals is Principal

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#commutative-algebra #ideals #maximal-and-prime-ideals #unique-factorization-domains
74
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Maximal and Prime Ideals

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#ring-theory #ideals #integral-domain #maximal-and-prime-ideals
179
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Only prime ideals of $\mathbb Z$ are $\{0\}$ and the principal ideals $p\mathbb Z$ for $p$ prime.

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#abstract-algebra #ring-theory #ideals #maximal-and-prime-ideals
4.4k
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What is the relationship between prime ideals and their generators?

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#abstract-algebra #ring-theory #ideals #maximal-and-prime-ideals #finitely-generated
455
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Uniqueness of maximal ideals in factor rings of formal power series

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#abstract-algebra #polynomials #ring-theory #maximal-and-prime-ideals #formal-power-series

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