List questions from maximal-and-prime-ideals

44

Views

Showing that $\pi(x)$ is not a prime in the ring $R=\Bbb Z[x]/I$ where $I$ is the ideal generated by $x^2+10$.

Published on 29 Apr 2020 - 23:50

311

Views

Number of ideals in the factor ring $\mathbb{Q}[x]/\langle x^4+3x^2+2 \rangle$

Published on 30 Apr 2020 - 7:40

92

Views

Basic Theorem about prime ideal

Published on 02 May 2020 - 23:52

38

Views

What is the difference between $7\mathbb{Z}$ and (7)?

Published on 05 May 2020 - 13:48

55

Views

Do the same rules apply to polynomial rings as to ring extensions?

Published on 27 Mar 2026 - 12:10

66

Views

Show that each of the ideals $I_k=\langle x_1,...,x_k\rangle$ in $F[x_1,...,x_n]$ for $1\leq k \leq n$ are prime and that each power is primary

Published on 08 May 2020 - 19:04

417

Views

$\mathbb{K}[x,y] /( xy - 1)$ has infinitely many prime ideals.

Published on 27 Mar 2026 - 22:11

242

Views

Classifying Ideal Class Group

Published on 25 Mar 2026 - 2:56

46

Views

Another Question Regarding Prime Ideals in $\mathbb{Q}[\sqrt{-199}]$

Published on 25 Mar 2026 - 3:00

924

Views

Prove$(2,x^2+x+1)$ is a maximal ideal of $\mathbb{Z}[x]$

Published on 10 May 2020 - 7:10

364

Views

If in a commutative ring $R$ a maximal ideal is nilpotent, then $R$ is local

Published on 25 Mar 2026 - 10:57

58

Views

Localization of Dedekind Domains

Published on 25 Mar 2026 - 17:43

45

Views

Primes containing a fixed element $f$ in a finitely generated $k$-algebra.

Published on 12 May 2020 - 15:37

416

Views

structure of ideals in lie algebra

Published on 27 Mar 2026 - 22:03

91

Views

equivalent definitions of ideals in non commutative, non associative algebra

Published on 14 May 2020 - 2:19

List Question

Showing that $\pi(x)$ is not a prime in the ring $R=\Bbb Z[x]/I$ where $I$ is the ideal generated by $x^2+10$.

Number of ideals in the factor ring $\mathbb{Q}[x]/\langle x^4+3x^2+2 \rangle$

Basic Theorem about prime ideal

What is the difference between $7\mathbb{Z}$ and (7)?

Do the same rules apply to polynomial rings as to ring extensions?

Show that each of the ideals $I_k=\langle x_1,...,x_k\rangle$ in $F[x_1,...,x_n]$ for $1\leq k \leq n$ are prime and that each power is primary

$\mathbb{K}[x,y] /( xy - 1)$ has infinitely many prime ideals.

Classifying Ideal Class Group

Another Question Regarding Prime Ideals in $\mathbb{Q}[\sqrt{-199}]$

Prove$(2,x^2+x+1)$ is a maximal ideal of $\mathbb{Z}[x]$

If in a commutative ring $R$ a maximal ideal is nilpotent, then $R$ is local

Localization of Dedekind Domains

Primes containing a fixed element $f$ in a finitely generated $k$-algebra.

structure of ideals in lie algebra

equivalent definitions of ideals in non commutative, non associative algebra

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