Question

Why is $k[x,y,z,u]/(x^2-y^2z, uy-x) \cong k[y,u]$?

score 108 · Answer 1 · 2026-04-16 13:34:33

108

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Why is $k[x,y,z,u]/(x^2-y^2z, uy-x) \cong k[y,u]$?

Published on 16 Apr 2026 - 13:34

score 39 · Answer 2 · 2026-04-13 07:40:12

39

Views

More Concrete Form for a Composite Field

Published on 13 Apr 2026 - 7:40

score 580 · Answer 3 · 2026-04-13 04:37:54

580

Views

Show that $\sqrt{-n}$ and $\sqrt{-n} +1$ are not prime in $\mathbb{Z}[\sqrt{-n} ]$

Published on 13 Apr 2026 - 4:37

score 100 · Answer 4 · 2026-04-15 07:17:28

100

Views

Must the product of a nil ideal with a minimal right ideal be 0?

Published on 15 Apr 2026 - 7:17

score 122 · Answer 5 · 2026-04-12 21:59:20

122

Views

$a,b \in R$ a ring. If $a | b$ in $R$ then $bR\subseteq aR$?

Published on 12 Apr 2026 - 21:59

score 121 · Answer 6 · 2026-04-15 19:51:30

121

Views

If there is a monomorphism between free $R$-modules $F \hookrightarrow G$, is the rank of $F$ necessarily less than or equal to the rank of $G$?

Published on 15 Apr 2026 - 19:51

score 331 · Answer 7 · 2026-04-16 21:10:57

331

Views

Find all units of $\Bbb Q[x] / (x^2-1)$

Published on 16 Apr 2026 - 21:10

score 65 · Answer 8 · 2026-04-17 15:19:23

65

Views

$g^l\in \langle f_1,\dots,f_k \rangle$, if the ideal generated by $f_1,\dots, f_k, gy -1$ in $\Bbb C[x_1,\dots,x_n, y]$ contains $1$

Published on 17 Apr 2026 - 15:19

score 50 · Answer 9 · 2026-04-13 21:00:52

50

Views

Are $x^2+1$ and $x+1$ the same in $\mathbb{Z}_2[x]$?

Published on 13 Apr 2026 - 21:00

score 78 · Answer 10 · 2026-04-14 17:45:09

78

Views

How many ideals contain $(x^2+1)$ in $\mathbb{Z}_4[x]$?

Published on 14 Apr 2026 - 17:45

score 384 · Answer 11 · 2026-04-11 13:14:12

384

Views

In UFD every irreducible element is prime

Published on 11 Apr 2026 - 13:14

score 81 · Answer 12 · 2026-04-25 16:15:51

81

Views

Sign of a permutation of a left coset G

Published on 25 Apr 2026 - 16:15

score 325 · Answer 13 · 2026-04-04 13:49:20

325

Views

ideal generated by minimal polynomial is maximal in $F[\alpha]$

Published on 04 Apr 2026 - 13:49

score 172 · Answer 14 · 2026-04-14 08:03:21

172

Views

What is a maximal ideal of the ring of polynomials of infinitely many variables?

Published on 14 Apr 2026 - 8:03

score 78 · Answer 15 · 2026-04-15 05:13:09

78

Views

Inclusions of representation rings $R(C_3;\mathbb{C})\hookrightarrow R(C_3;\mathbb{H})$

Published on 15 Apr 2026 - 5:13

List Question

Why is $k[x,y,z,u]/(x^2-y^2z, uy-x) \cong k[y,u]$?

More Concrete Form for a Composite Field

Show that $\sqrt{-n}$ and $\sqrt{-n} +1$ are not prime in $\mathbb{Z}[\sqrt{-n} ]$

Must the product of a nil ideal with a minimal right ideal be 0?

$a,b \in R$ a ring. If $a | b$ in $R$ then $bR\subseteq aR$?

If there is a monomorphism between free $R$-modules $F \hookrightarrow G$, is the rank of $F$ necessarily less than or equal to the rank of $G$?

Find all units of $\Bbb Q[x] / (x^2-1)$

$g^l\in \langle f_1,\dots,f_k \rangle$, if the ideal generated by $f_1,\dots, f_k, gy -1$ in $\Bbb C[x_1,\dots,x_n, y]$ contains $1$

Are $x^2+1$ and $x+1$ the same in $\mathbb{Z}_2[x]$?

How many ideals contain $(x^2+1)$ in $\mathbb{Z}_4[x]$?

In UFD every irreducible element is prime

Sign of a permutation of a left coset G

ideal generated by minimal polynomial is maximal in $F[\alpha]$

What is a maximal ideal of the ring of polynomials of infinitely many variables?

Inclusions of representation rings $R(C_3;\mathbb{C})\hookrightarrow R(C_3;\mathbb{H})$

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