Question

Show that $\Bbb Q$ is not a finitely generated $\Bbb Z$-algebra.

score 736 · Answer 1 · 2026-03-24 23:44:57

736

Views

Show that $\Bbb Q$ is not a finitely generated $\Bbb Z$-algebra.

Published on 24 Mar 2026 - 23:44

score 37 · Answer 2 · 2018-04-28 23:59:43

37

Views

$h$ is a homomorphism, $f$ is any map and $a \neq b$. Then $h(f(a)) \neq h(f(b)) \implies f(a) \neq f(b)$

Published on 28 Apr 2018 - 23:59

score 435 · Answer 3 · 2026-03-25 01:26:17

435

Views

Tensor product of noetherian modules is also noetherian?

Published on 25 Mar 2026 - 1:26

score 1k · Answer 4 · 2018-04-29 04:05:39

1k

Views

Show that for any commutative ring $R$, $R[X] \otimes R[Y] \simeq R[X,Y]$.

Published on 29 Apr 2018 - 4:05

score 71 · Answer 5 · 2018-04-29 06:37:06

71

Views

How does $S \otimes_R A$ become an $S$-algebra?

Published on 29 Apr 2018 - 6:37

score 904 · Answer 6 · 2018-04-29 09:35:28

904

Views

Find a basis for the submodule $\mathbb Z^3$ consisting of all integer solutions of the system of equations $x+2y+3z=0, x+4y+9z=0$

Published on 29 Apr 2018 - 9:35

score 220 · Answer 7 · 2026-03-22 22:28:26

220

Views

Interpretation of preadditive categories as rings.

Published on 22 Mar 2026 - 22:28

score 482 · Answer 8 · 2018-04-29 22:15:08

482

Views

Order of elements in free $\mathbb{Z}$ module

Published on 29 Apr 2018 - 22:15

score 1k · Answer 9 · 2026-03-25 00:06:36

1k

Views

Surjectivity of a map on inverse limits

Published on 25 Mar 2026 - 0:06

score 34 · Answer 10 · 2018-04-30 10:06:12

34

Views

Realize $M \otimes_A N$ is an $B-$ module where $M$ is an $A$ module and $N$ is an $AB$ bimodule

Published on 30 Apr 2018 - 10:06

score 418 · Answer 11 · 2026-03-22 21:14:34

418

Views

Example of reduced module

Published on 22 Mar 2026 - 21:14

score 998 · Answer 12 · 2018-04-30 14:40:15

998

Views

Does a finitely generated module have finite rank?

Published on 30 Apr 2018 - 14:40

score 29 · Answer 13 · 2018-04-30 14:51:49

29

Views

Proof verification: Let $N,P_1,P_2$ be submodules of $M$, show that $P_1 = P_2$

Published on 30 Apr 2018 - 14:51

score 195 · Answer 14 · 2018-04-30 15:48:37

195

Views

Projective module that isn't free

Published on 30 Apr 2018 - 15:48

score 259 · Answer 15 · 2026-03-25 03:03:46

259

Views

Why $\mathrm{Ext}^n_{R[t]}(X, Y)\simeq\mathrm{Ext}^n_R(X, Y)\oplus\mathrm{Ext}^{n-1}_R(X, Y)$?

Published on 25 Mar 2026 - 3:03

List Question

Show that $\Bbb Q$ is not a finitely generated $\Bbb Z$-algebra.

$h$ is a homomorphism, $f$ is any map and $a \neq b$. Then $h(f(a)) \neq h(f(b)) \implies f(a) \neq f(b)$

Tensor product of noetherian modules is also noetherian?

Show that for any commutative ring $R$, $R[X] \otimes R[Y] \simeq R[X,Y]$.

How does $S \otimes_R A$ become an $S$-algebra?

Find a basis for the submodule $\mathbb Z^3$ consisting of all integer solutions of the system of equations $x+2y+3z=0, x+4y+9z=0$

Interpretation of preadditive categories as rings.

Order of elements in free $\mathbb{Z}$ module

Surjectivity of a map on inverse limits

Realize $M \otimes_A N$ is an $B-$ module where $M$ is an $A$ module and $N$ is an $AB$ bimodule

Example of reduced module

Does a finitely generated module have finite rank?

Proof verification: Let $N,P_1,P_2$ be submodules of $M$, show that $P_1 = P_2$

Projective module that isn't free

Why $\mathrm{Ext}^n_{R[t]}(X, Y)\simeq\mathrm{Ext}^n_R(X, Y)\oplus\mathrm{Ext}^{n-1}_R(X, Y)$?

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