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Spectrum of the ring of formal power series over integers

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#algebraic-geometry #ring-theory #commutative-algebra #maximal-and-prime-ideals #formal-power-series
136
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There exists a prime ideal not containing non-nilpotent element

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#abstract-algebra #ring-theory #ideals #maximal-and-prime-ideals
33
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Do the maps of rings coincide under the condition of reducedness and localization assumption?

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#ring-theory #commutative-algebra #maximal-and-prime-ideals #localization
307
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$\mathrm{Ass}(M)$ is finite

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#abstract-algebra #commutative-algebra #modules #maximal-and-prime-ideals
49
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Prime ideals of a subring of $A\times B$

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#abstract-algebra #ring-theory #commutative-algebra #maximal-and-prime-ideals
155
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On minimal elements, w.r.t. inclusion, of non-empty subset of prime ideals of commutative rings

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#commutative-algebra #maximal-and-prime-ideals #zariski-topology #artinian
166
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Irreducibility of generators of maximal ideal

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#commutative-algebra #maximal-and-prime-ideals
207
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Is $x$ always irreducible in the quotient ring

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#commutative-algebra #irreducible-polynomials #maximal-and-prime-ideals
67
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When does $\mathbb{Z}[\zeta_m]$ contain divisors of $2$ (besides units)?

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#abstract-algebra #ring-theory #maximal-and-prime-ideals #pythagorean-triples #ring-homomorphism
89
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Two steps in proving that $\operatorname{Ass }M\subset \operatorname{Ass} M'\cup\operatorname{Ass} M''$

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#abstract-algebra #commutative-algebra #modules #maximal-and-prime-ideals
535
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The notion of $P$-primary component

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#abstract-algebra #commutative-algebra #maximal-and-prime-ideals #primary-decomposition
176
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What are the prime ideals of the polynomial ring $\mathbb{R}[x]$?

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#irreducible-polynomials #maximal-and-prime-ideals
40
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Why is $p_x = \mathcal I_V \left ( \{(x_1,x_2, \dots ,x_n) \} \right )$ a prime ideal?

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#algebraic-geometry #commutative-algebra #maximal-and-prime-ideals
559
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Nilradical is the intersection of finitely many minimal prime ideals.

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#commutative-algebra #maximal-and-prime-ideals #nilpotence
237
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Prime ideals in $\mathbb{Z}[X], \mathbb{Q}[X], \mathbb{F}_{19}[X]$.

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#abstract-algebra #ring-theory #maximal-and-prime-ideals #unique-factorization-domains #polynomial-rings

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