Question

Show that the field of quotients of $\mathbb{Z}[2i]$ is $\mathbb{Q}[i]$

score 239 · Answer 1 · 2026-04-12 02:08:15

239

Views

Show that the field of quotients of $\mathbb{Z}[2i]$ is $\mathbb{Q}[i]$

Published on 12 Apr 2026 - 2:08

score 752 · Answer 2 · 2026-04-14 07:10:00

752

Views

Let $K$ be a field containing an integral domain $D$ and $F$ be the field of quotients of $D$. Then $K$ contains a field isomorphic to $F$.

Published on 14 Apr 2026 - 7:10

score 92 · Answer 3 · 2026-04-17 15:14:53

92

Views

Show that the set $P_F$ of all polynomial functions on $F$ forms a subring of $F^F$. using the subring test

Published on 17 Apr 2026 - 15:14

score 426 · Answer 4 · 2026-04-17 08:48:20

426

Views

Let $D$ be an integral domain $a,b \in D$. $m,n$ are relatively prime and $a^n=b^n$ and $a^m=b^m \implies a=b$.

Published on 17 Apr 2026 - 8:48

score 93 · Answer 5 · 2026-04-16 20:51:42

93

Views

Prove that $\mathbb{Z}[i]/\langle 2+i \rangle = \{\overline{0}, \overline{1}, \overline{2}, \overline{3}, \overline{4}\}$.

Published on 16 Apr 2026 - 20:51

score 50 · Answer 6 · 2026-05-10 20:37:35

50

Views

usual method of argument in the linkage theory

Published on 10 May 2026 - 20:37

score 98 · Answer 7 · 2026-04-08 16:29:22

98

Views

Reference for introduction to algebraic linkage theory

Published on 08 Apr 2026 - 16:29

score 64 · Answer 8 · 2026-04-10 18:43:11

64

Views

Non-commutative unitary rings

Published on 10 Apr 2026 - 18:43

score 283 · Answer 9 · 2026-04-12 06:40:27

283

Views

Equivalence of modules over different rings

Published on 12 Apr 2026 - 6:40

score 195 · Answer 10 · 2026-04-16 05:43:27

195

Views

Prove that $(x-1,y-1)$ is a prime ideal in $\mathbb F_2[x,y]$

Published on 16 Apr 2026 - 5:43

score 662 · Answer 11 · 2026-04-15 04:09:21

662

Views

Non commutative ring of order 4

Published on 15 Apr 2026 - 4:09

score 74 · Answer 12 · 2026-05-11 05:19:22

74

Views

Does every finite dimensional algebra contains a semisimple subalgebra?

Published on 11 May 2026 - 5:19

score 272 · Answer 13 · 2026-04-13 17:21:22

272

Views

Prove that $\det (AB)=\det A \det B$ when entries of the matrices are in a non-commutative ring $R$

Published on 13 Apr 2026 - 17:21

score 81 · Answer 14 · 2026-04-16 22:54:08

81

Views

Show that $\mathbb{F}_p[x]/ ⟨f(x)⟩$ is a field of characteristic $p$

Published on 16 Apr 2026 - 22:54

score 112 · Answer 15 · 2026-04-16 16:49:03

112

Views

If $\mathrm{Ext}^n_R (M,R/\mathrm{rad}(R))=0$ for all $n\geq 1$, then $\mathrm{Ext}^n_R (M,N)=0$ for all $n\geq 1$.

Published on 16 Apr 2026 - 16:49

List Question

Show that the field of quotients of $\mathbb{Z}[2i]$ is $\mathbb{Q}[i]$

Let $K$ be a field containing an integral domain $D$ and $F$ be the field of quotients of $D$. Then $K$ contains a field isomorphic to $F$.

Show that the set $P_F$ of all polynomial functions on $F$ forms a subring of $F^F$. using the subring test

Let $D$ be an integral domain $a,b \in D$. $m,n$ are relatively prime and $a^n=b^n$ and $a^m=b^m \implies a=b$.

Prove that $\mathbb{Z}[i]/\langle 2+i \rangle = \{\overline{0}, \overline{1}, \overline{2}, \overline{3}, \overline{4}\}$.

usual method of argument in the linkage theory

Reference for introduction to algebraic linkage theory

Non-commutative unitary rings

Equivalence of modules over different rings

Prove that $(x-1,y-1)$ is a prime ideal in $\mathbb F_2[x,y]$

Non commutative ring of order 4

Does every finite dimensional algebra contains a semisimple subalgebra?

Prove that $\det (AB)=\det A \det B$ when entries of the matrices are in a non-commutative ring $R$

Show that $\mathbb{F}_p[x]/ ⟨f(x)⟩$ is a field of characteristic $p$

If $\mathrm{Ext}^n_R (M,R/\mathrm{rad}(R))=0$ for all $n\geq 1$, then $\mathrm{Ext}^n_R (M,N)=0$ for all $n\geq 1$.

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