Question

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

score 113 · Answer 1 · 2026-03-26 02:45:54

113

Views

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

Published on 26 Mar 2026 - 2:45

score 206 · Answer 2 · 2026-03-26 02:44:32

206

Views

Faithfully flat module and exact sequences

Published on 26 Mar 2026 - 2:44

score 56 · Answer 3 · 2026-03-26 02:46:57

56

Views

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

Published on 26 Mar 2026 - 2:46

score 237 · Answer 4 · 2026-03-26 02:45:55

237

Views

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

Published on 26 Mar 2026 - 2:45

score 724 · Answer 5 · 2026-03-26 02:46:55

724

Views

Quotient of polynomial ring flat $R$-algebra

Published on 26 Mar 2026 - 2:46

score 128 · Answer 6 · 2026-03-26 02:44:36

128

Views

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

Published on 26 Mar 2026 - 2:44

score 159 · Answer 7 · 2026-03-26 02:51:30

159

Views

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

Published on 26 Mar 2026 - 2:51

score 332 · Answer 8 · 2026-03-26 02:51:27

332

Views

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

Published on 26 Mar 2026 - 2:51

score 105 · Answer 9 · 2026-03-26 02:47:53

105

Views

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

Published on 26 Mar 2026 - 2:47

score 49 · Answer 10 · 2026-03-26 02:45:52

49

Views

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

Published on 26 Mar 2026 - 2:45

score 197 · Answer 11 · 2026-03-26 02:46:55

197

Views

surjectivity condition for induced map of prime ideals

Published on 26 Mar 2026 - 2:46

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 65 · Answer 13 · 2026-03-26 02:46:55

65

Views

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

Published on 26 Mar 2026 - 2:46

score 197 · Answer 14 · 2026-03-26 02:45:39

197

Views

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

Published on 26 Mar 2026 - 2:45

score 156 · Answer 15 · 2026-05-06 13:23:22

156

Views

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

Published on 06 May 2026 - 13:23

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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