Question

If $A,B,C$ are f.g. $\mathbf{Z}/p^n\mathbf{Z}$-modules and $A\oplus C\cong B\oplus C$, show $A\cong B$.

score 154 · Answer 1 · 2026-03-25 11:16:38

154

Views

If $A,B,C$ are f.g. $\mathbf{Z}/p^n\mathbf{Z}$-modules and $A\oplus C\cong B\oplus C$, show $A\cong B$.

Published on 25 Mar 2026 - 11:16

score 102 · Answer 2 · 2018-08-20 04:54:15

102

Views

Why $ S^{-1}R $ is local if and only if the saturation of $ S $ (set of divisors of elements of $ S $) is the complement of a prime ideal?

Published on 20 Aug 2018 - 4:54

score 303 · Answer 3 · 2018-08-20 17:19:24

303

Views

Prove or disprove that $Z(z^2-xy)$ is isomorphic to $\mathbb{A^2}$

Published on 20 Aug 2018 - 17:19

score 56 · Answer 4 · 2026-03-29 08:21:04

56

Views

non-terminating descending chain of non-finitely generated ideals

Published on 29 Mar 2026 - 8:21

score 445 · Answer 5 · 2018-08-21 01:36:50

445

Views

On Atiyah-Macdonald Exercise 3.26

Published on 21 Aug 2018 - 1:36

score 782 · Answer 6 · 2026-03-25 06:06:19

782

Views

Show that the ring of polynomials with coefficients in a field, and in infinitely many variables, is not Noetherian

Published on 25 Mar 2026 - 6:06

score 90 · Answer 7 · 2018-08-21 10:04:03

90

Views

Polynomial analogue of $p$-adic numbers

Published on 21 Aug 2018 - 10:04

score 229 · Answer 8 · 2026-03-27 13:29:17

229

Views

Linearly independence on Kronecker products

Published on 27 Mar 2026 - 13:29

score 114 · Answer 9 · 2018-08-21 22:17:44

114

Views

Does a flat limit of non-degenerate schemes become degenerate?

Published on 21 Aug 2018 - 22:17

score 156 · Answer 10 · 2018-08-22 12:35:47

156

Views

Dimension of Affine Scheme of Integral Domain

Published on 22 Aug 2018 - 12:35

score 84 · Answer 11 · 2018-08-22 18:50:35

84

Views

Integral extensions of the ring of multivariate polynomials

Published on 22 Aug 2018 - 18:50

score 416 · Answer 12 · 2026-03-25 06:12:42

416

Views

Zariski topology and product topology on $\mathbb A_k^m \times \mathbb A_k^n$

Published on 25 Mar 2026 - 6:12

score 392 · Answer 13 · 2026-03-25 21:49:04

392

Views

Application Hilbert's Nullstellensatz for $k$-algebra of finite type

Published on 25 Mar 2026 - 21:49

score 46 · Answer 14 · 2018-08-23 08:40:50

46

Views

Why the function field of an algebraic curve $f(x,y)=0$ can be identified with $\overline{L}(x)[y]/(f)$?

Published on 23 Aug 2018 - 8:40

score 100 · Answer 15 · 2026-03-31 17:52:20

100

Views

A faithful ideal in a Noetherian ring is a regular ideal

Published on 31 Mar 2026 - 17:52

List Question

If $A,B,C$ are f.g. $\mathbf{Z}/p^n\mathbf{Z}$-modules and $A\oplus C\cong B\oplus C$, show $A\cong B$.

Why $ S^{-1}R $ is local if and only if the saturation of $ S $ (set of divisors of elements of $ S $) is the complement of a prime ideal?

Prove or disprove that $Z(z^2-xy)$ is isomorphic to $\mathbb{A^2}$

non-terminating descending chain of non-finitely generated ideals

On Atiyah-Macdonald Exercise 3.26

Show that the ring of polynomials with coefficients in a field, and in infinitely many variables, is not Noetherian

Polynomial analogue of $p$-adic numbers

Linearly independence on Kronecker products

Does a flat limit of non-degenerate schemes become degenerate?

Dimension of Affine Scheme of Integral Domain

Integral extensions of the ring of multivariate polynomials

Zariski topology and product topology on $\mathbb A_k^m \times \mathbb A_k^n$

Application Hilbert's Nullstellensatz for $k$-algebra of finite type

Why the function field of an algebraic curve $f(x,y)=0$ can be identified with $\overline{L}(x)[y]/(f)$?

A faithful ideal in a Noetherian ring is a regular ideal

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