Question

Given that $B$ is a flat $A$-algebra, why is the following an exact sequence of $B$-modules

score 65 · Answer 1 · 2026-03-26 01:07:53

65

Views

Given that $B$ is a flat $A$-algebra, why is the following an exact sequence of $B$-modules

Published on 26 Mar 2026 - 1:07

score 169 · Answer 2 · 2026-05-10 14:58:10

169

Views

Composition of flat morphisms is flat

Published on 10 May 2026 - 14:58

score 114 · Answer 3 · 2026-03-26 01:04:42

114

Views

Show the following properties of $A$ as an $R$-algebra

Published on 26 Mar 2026 - 1:04

score 45 · Answer 4 · 2026-03-26 01:00:08

45

Views

Show that $A$ is a flat $R$-module

Published on 26 Mar 2026 - 1:00

score 132 · Answer 5 · 2026-03-26 01:04:33

132

Views

Ideal $J$ in a Noetherian local domain such that the natural map $J \otimes_R J \to J^2$ is an isomorphism

Published on 26 Mar 2026 - 1:04

score 214 · Answer 6 · 2026-03-26 01:04:33

214

Views

Flatness of $A=F[x_1,\dots,x_n]/\langle f_1,\dots,f_k \rangle$

Published on 26 Mar 2026 - 1:04

score 99 · Answer 7 · 2026-03-26 01:04:32

99

Views

Flatness of $\frac{A[b]}{\langle u,v \rangle}$ over $A$ and flatness of $\frac{A[w]}{\langle u \rangle}$ over $A$

Published on 26 Mar 2026 - 1:04

score 82 · Answer 8 · 2026-04-16 18:06:11

82

Views

Flatness of $\frac{R[T]}{I}$ over $R$ implies that $I$ is principal or $I=R[T]$?

Published on 16 Apr 2026 - 18:06

score 174 · Answer 9 · 2026-03-26 01:04:34

174

Views

Morphism $\operatorname{Spec}(K) \to \operatorname{Spec}(K[x]/(x^2))$ is not flat under any restriction to open subset

Published on 26 Mar 2026 - 1:04

score 62 · Answer 10 · 2026-03-26 01:04:36

62

Views

$A$-flatness of $\frac{B}{\langle b_i \rangle}$, $A \subseteq B=A[b]$, implies $A$-flatness of $\frac{B}{\langle b_1,b_2 \rangle}$?

Published on 26 Mar 2026 - 1:04

score 72 · Answer 11 · 2026-03-26 01:04:39

72

Views

When flatness of $S$ over $R_i$ implies flatness of $S$ over the ring generated by $R_1,R_2$

Published on 26 Mar 2026 - 1:04

score 155 · Answer 12 · 2026-03-26 01:03:36

155

Views

Restriction of flat morphism to preimage of open subscheme.

Published on 26 Mar 2026 - 1:03

score 72 · Answer 13 · 2026-03-26 01:01:14

72

Views

Flatness of a certain ring extension

Published on 26 Mar 2026 - 1:01

score 33 · Answer 14 · 2026-05-10 19:19:19

33

Views

Lifting a complete intersection in $\mathbb{P}^n_{\mathbb{F}_p}$ to $\mathbb{Z}_p$

Published on 10 May 2026 - 19:19

score 84 · Answer 15 · 2026-03-26 01:00:36

84

Views

Concerning $\langle p,q \rangle \subseteq k[p,q]$

Published on 26 Mar 2026 - 1:00

List Question

Given that $B$ is a flat $A$-algebra, why is the following an exact sequence of $B$-modules

Composition of flat morphisms is flat

Show the following properties of $A$ as an $R$-algebra

Show that $A$ is a flat $R$-module

Ideal $J$ in a Noetherian local domain such that the natural map $J \otimes_R J \to J^2$ is an isomorphism

Flatness of $A=F[x_1,\dots,x_n]/\langle f_1,\dots,f_k \rangle$

Flatness of $\frac{A[b]}{\langle u,v \rangle}$ over $A$ and flatness of $\frac{A[w]}{\langle u \rangle}$ over $A$

Flatness of $\frac{R[T]}{I}$ over $R$ implies that $I$ is principal or $I=R[T]$?

Morphism $\operatorname{Spec}(K) \to \operatorname{Spec}(K[x]/(x^2))$ is not flat under any restriction to open subset

$A$-flatness of $\frac{B}{\langle b_i \rangle}$, $A \subseteq B=A[b]$, implies $A$-flatness of $\frac{B}{\langle b_1,b_2 \rangle}$?

When flatness of $S$ over $R_i$ implies flatness of $S$ over the ring generated by $R_1,R_2$

Restriction of flat morphism to preimage of open subscheme.

Flatness of a certain ring extension

Lifting a complete intersection in $\mathbb{P}^n_{\mathbb{F}_p}$ to $\mathbb{Z}_p$

Concerning $\langle p,q \rangle \subseteq k[p,q]$

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