List questions from ideals

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Compute the transcendence degree (transcendence degree and tensor products)

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Example of ring with two maximal ideals such that the char of the quotients is $0$, respectively $p$.

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Ideals, Dedekind domain and $\mathbb{Z}[\sqrt{-3}]$

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Meaning of $S^{-1}R$ notation

Published on 04 Oct 2014 - 16:30

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Maximal Ideals in $R=\{a+bi:a,b\in \mathbb Z\}$

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Is the set of polynomials an $x^n+ a_{n-1}x^{n-1}+\ldots+a_1x +a_0$ such that $2^k+1$ divides $a_k$ an ideal in $\Bbb Z[x]$?

Published on 05 Oct 2014 - 7:10

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Does $ax\in\mathfrak{m}I$ with $x\in I\setminus\mathfrak{m}I$ and $a \in R$ imply $a\in\mathfrak{m}$ for an invertible fractional $R$-ideal $I$?

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Nonzero Prime Ideals are Maximal in Euclidean Domains

Published on 08 Oct 2014 - 20:56

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Prime ideals of Z

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Factorization in noetherian domains

Published on 10 Oct 2014 - 13:45

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Primary decomposition of $(XY,(X-Y)Z)$ in $k[X,Y,Z]$

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Primality of homogeneous ideal

Published on 11 Oct 2014 - 7:43

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Unique maximal ideal in the ring of fraction

Published on 12 Oct 2014 - 20:29

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Localizing at maximal ideals and the product

Published on 13 Oct 2014 - 2:15

List Question

Prime ideals in $k[x,y]/(xy-1)$.

Compute the transcendence degree (transcendence degree and tensor products)

Example of ring with two maximal ideals such that the char of the quotients is $0$, respectively $p$.

Ideals, Dedekind domain and $\mathbb{Z}[\sqrt{-3}]$

Meaning of $S^{-1}R$ notation

Maximal Ideals in $R=\{a+bi:a,b\in \mathbb Z\}$

Is the set of polynomials an $x^n+ a_{n-1}x^{n-1}+\ldots+a_1x +a_0$ such that $2^k+1$ divides $a_k$ an ideal in $\Bbb Z[x]$?

Does $ax\in\mathfrak{m}I$ with $x\in I\setminus\mathfrak{m}I$ and $a \in R$ imply $a\in\mathfrak{m}$ for an invertible fractional $R$-ideal $I$?

Nonzero Prime Ideals are Maximal in Euclidean Domains

Prime ideals of Z

Factorization in noetherian domains

Primary decomposition of $(XY,(X-Y)Z)$ in $k[X,Y,Z]$

Primality of homogeneous ideal

Unique maximal ideal in the ring of fraction

Localizing at maximal ideals and the product

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