Question

Is it true "If $X \subset Y$ then $\Bbb I(Y) \subset \Bbb I(X)$"(proper inclusion)?

score 48 · Answer 1 · 2019-02-11 19:09:44

48

Views

Is it true "If $X \subset Y$ then $\Bbb I(Y) \subset \Bbb I(X)$"(proper inclusion)?

Published on 11 Feb 2019 - 19:09

score 376 · Answer 2 · 2026-03-26 03:01:36

376

Views

The localization of an ideal is equal to the localization of the ring

Published on 26 Mar 2026 - 3:01

score 172 · Answer 3 · 2019-02-12 07:50:59

172

Views

For an integral domain $R$, the rings $R\times R $ and $R\times R\times R$ are not isomorphic

Published on 12 Feb 2019 - 7:50

score 1k · Answer 4 · 2026-03-28 04:53:22

1k

Views

How to find the generator of the following ideals?

Published on 28 Mar 2026 - 4:53

score 40 · Answer 5 · 2019-02-12 14:02:48

40

Views

Polynomial Ring modulo Ideal is Polynomial ring of cosets of indeterminates.

Published on 12 Feb 2019 - 14:02

score 151 · Answer 6 · 2019-02-12 18:43:10

151

Views

Is $(a)/(a^2)\cong R/(a)$, or something else? ; For ideals $(a), (a^2)\leq R$

Published on 12 Feb 2019 - 18:43

score 349 · Answer 7 · 2026-03-28 12:02:40

349

Views

How to determine the kernel $\ker \varepsilon_{\sqrt 2}$ and the image $\varepsilon_{\sqrt 2}(\mathbb Q[X])?$

Published on 28 Mar 2026 - 12:02

score 50 · Answer 8 · 2019-02-13 02:18:13

50

Views

Suppose $f,g\in \sqrt{I} \subseteq K[x]$ such that $in(f)>in(g)$. Then $g\in I$.

Published on 13 Feb 2019 - 2:18

score 365 · Answer 9 · 2026-03-25 14:06:18

365

Views

On a colon ideal in the polynomial ring $\mathbb R[x,y]$

Published on 25 Mar 2026 - 14:06

score 94 · Answer 10 · 2026-03-25 07:41:37

94

Views

Does the vector space spanned by a Gröbner basis depend on the monomial order?

Published on 25 Mar 2026 - 7:41

score 103 · Answer 11 · 2019-02-16 03:23:36

103

Views

Show that $\Bbb Z[\alpha,4/\alpha]/(2)$ is a direct product of three domains, where $\alpha^3+\alpha^2-2\alpha+8=0$

Published on 16 Feb 2019 - 3:23

score 50 · Answer 12 · 2026-03-25 11:03:21

50

Views

Find a homomorphism that maps a point in a Boolean algebra into the image of a proper filter

Published on 25 Mar 2026 - 11:03

score 62 · Answer 13 · 2026-03-29 04:41:29

62

Views

How to prove that $\dim_k(k[x_1,\dotsc,x_n]/\sqrt{I})=|V(I)|$?

Published on 29 Mar 2026 - 4:41

score 1.4k · Answer 14 · 2026-03-29 04:48:50

1.4k

Views

Ideal generated by two elements is maximal in $\mathbb{Z}[x]$

Published on 29 Mar 2026 - 4:48

score 84 · Answer 15 · 2019-02-18 01:30:51

84

Views

Ideal of $\mathbb{Z}[x]$ generated by $3$ and $x^2+1$ is proper

Published on 18 Feb 2019 - 1:30

List Question

Is it true "If $X \subset Y$ then $\Bbb I(Y) \subset \Bbb I(X)$"(proper inclusion)?

The localization of an ideal is equal to the localization of the ring

For an integral domain $R$, the rings $R\times R $ and $R\times R\times R$ are not isomorphic

How to find the generator of the following ideals?

Polynomial Ring modulo Ideal is Polynomial ring of cosets of indeterminates.

Is $(a)/(a^2)\cong R/(a)$, or something else? ; For ideals $(a), (a^2)\leq R$

How to determine the kernel $\ker \varepsilon_{\sqrt 2}$ and the image $\varepsilon_{\sqrt 2}(\mathbb Q[X])?$

Suppose $f,g\in \sqrt{I} \subseteq K[x]$ such that $in(f)>in(g)$. Then $g\in I$.

On a colon ideal in the polynomial ring $\mathbb R[x,y]$

Does the vector space spanned by a Gröbner basis depend on the monomial order?

Show that $\Bbb Z[\alpha,4/\alpha]/(2)$ is a direct product of three domains, where $\alpha^3+\alpha^2-2\alpha+8=0$

Find a homomorphism that maps a point in a Boolean algebra into the image of a proper filter

How to prove that $\dim_k(k[x_1,\dotsc,x_n]/\sqrt{I})=|V(I)|$?

Ideal generated by two elements is maximal in $\mathbb{Z}[x]$

Ideal of $\mathbb{Z}[x]$ generated by $3$ and $x^2+1$ is proper

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