Question

Natural map $M\rightarrow M\otimes_R R'$ injective - Missing prerequisite in Bosch's book?

score 112 · Answer 1 · 2020-03-17 14:46:23

112

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Natural map $M\rightarrow M\otimes_R R'$ injective - Missing prerequisite in Bosch's book?

Published on 17 Mar 2020 - 14:46

score 205 · Answer 2 · 2020-03-20 05:20:24

205

Views

Faithfully flat module and exact sequences

Published on 20 Mar 2020 - 5:20

score 55 · Answer 3 · 2020-04-14 21:36:57

55

Views

If $B$ is a flat $A$-algebra then $B_{\mathrm{red}}$ is a flat $A_{\mathrm{red}}$-algebra

Published on 14 Apr 2020 - 21:36

score 236 · Answer 4 · 2020-04-30 22:27:19

236

Views

$\operatorname{Hom}_B$ of flat modules is flat over $A$?

Published on 30 Apr 2020 - 22:27

score 723 · Answer 5 · 2020-05-08 01:40:47

723

Views

Quotient of polynomial ring flat $R$-algebra

Published on 08 May 2020 - 1:40

score 127 · Answer 6 · 2020-05-09 20:20:21

127

Views

Polynomial map $K[t] \to K[t]$ induces flat module structure

Published on 09 May 2020 - 20:20

score 158 · Answer 7 · 2020-05-17 00:17:42

158

Views

When is relative Hilbert scheme $\text{Hilb}_{X/S}^{p(t)}$ flat over $S$?

Published on 17 May 2020 - 0:17

score 331 · Answer 8 · 2020-05-17 11:38:24

331

Views

Is the affine cone of a flat projective scheme again flat?

Published on 17 May 2020 - 11:38

score 104 · Answer 9 · 2020-05-21 18:26:13

104

Views

When is $K[X_1,X_2,...,X_n] \to K[Y_1,Y_2,...,Y_m]$ a flat morphism

Published on 21 May 2020 - 18:26

score 48 · Answer 10 · 2020-05-23 18:49:25

48

Views

Flatness of the $p$-th power roots ideals in a perfect ring

Published on 23 May 2020 - 18:49

score 196 · Answer 11 · 2020-05-23 21:39:45

196

Views

surjectivity condition for induced map of prime ideals

Published on 23 May 2020 - 21:39

score 165 · Answer 12 · 2026-03-25 12:28:11

165

Views

Flat extension of local rings with a specified extension of residue field

Published on 25 Mar 2026 - 12:28

score 64 · Answer 13 · 2020-05-29 14:46:33

64

Views

Why this flatness condition is needed? (Serge lang's Algebra)(p.618, chapter 16, proposition 3.7)

Published on 29 May 2020 - 14:46

score 196 · Answer 14 · 2020-05-31 16:34:49

196

Views

Is $k[x,xy] \subseteq k[x,y]$ a flat ring extension?

Published on 31 May 2020 - 16:34

score 154 · Answer 15 · 2026-02-23 08:05:04

154

Views

$A \subset B$ be a faithfully flat extension of domains and $B$ is integrally closed then $A$ is also integrally closed.

Published on 23 Feb 2026 - 8:05

List Question

Natural map $M\rightarrow M\otimes_R R'$ injective - Missing prerequisite in Bosch's book?

Faithfully flat module and exact sequences

If $B$ is a flat $A$-algebra then $B_{\mathrm{red}}$ is a flat $A_{\mathrm{red}}$-algebra

$\operatorname{Hom}_B$ of flat modules is flat over $A$?

Quotient of polynomial ring flat $R$-algebra

Polynomial map $K[t] \to K[t]$ induces flat module structure

When is relative Hilbert scheme $\text{Hilb}_{X/S}^{p(t)}$ flat over $S$?

Is the affine cone of a flat projective scheme again flat?

When is $K[X_1,X_2,...,X_n] \to K[Y_1,Y_2,...,Y_m]$ a flat morphism

Flatness of the $p$-th power roots ideals in a perfect ring

surjectivity condition for induced map of prime ideals

Flat extension of local rings with a specified extension of residue field

Why this flatness condition is needed? (Serge lang's Algebra)(p.618, chapter 16, proposition 3.7)

Is $k[x,xy] \subseteq k[x,y]$ a flat ring extension?

$A \subset B$ be a faithfully flat extension of domains and $B$ is integrally closed then $A$ is also integrally closed.

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