Question

how to prove a graded version of Nakayama's lemma

score 635 · Answer 1 · 2026-03-29 18:53:39

635

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how to prove a graded version of Nakayama's lemma

Published on 29 Mar 2026 - 18:53

score 153 · Answer 2 · 2018-10-21 16:02:55

153

Views

In a ring with no nilpotent elements (0) is not decomposable.

Published on 21 Oct 2018 - 16:02

score 107 · Answer 3 · 2026-03-28 05:23:27

107

Views

Is there accepted notation for the homogeneous part of highest degree, and is there a name for "pseudodivision"?

Published on 28 Mar 2026 - 5:23

score 36 · Answer 4 · 2026-03-26 01:10:19

36

Views

What is $S^{-1}N$ in $S^{-1}M$?

Published on 26 Mar 2026 - 1:10

score 319 · Answer 5 · 2026-04-02 00:22:10

319

Views

Is the quotient ring $K[x]/\langle f\rangle$ a $n$-dimensional $K$-vector space?

Published on 02 Apr 2026 - 0:22

score 530 · Answer 6 · 2026-02-23 02:30:31

530

Views

If sum and product of elements are integral, they must be integral

Published on 23 Feb 2026 - 2:30

score 486 · Answer 7 · 2026-03-25 23:38:28

486

Views

A question about $S^{-1}R\otimes_R M\cong S^{-1}M$ as $S^{-1}R$-modules

Published on 25 Mar 2026 - 23:38

score 1.2k · Answer 8 · 2026-04-02 00:22:49

1.2k

Views

Do subrings contain 0, the additive identity because $1-1=0$ in subrings as in subfields?

Published on 02 Apr 2026 - 0:22

score 125 · Answer 9 · 2026-03-26 01:12:41

125

Views

Minimal prime of a ring is contraction of some prime ideal of any extension of the ring.

Published on 26 Mar 2026 - 1:12

score 256 · Answer 10 · 2026-03-29 18:50:34

256

Views

Proving an $R$-module isomorphism is in fact an $R/I$-module isomorphism using universal properties.

Published on 29 Mar 2026 - 18:50

score 47 · Answer 11 · 2026-03-29 15:03:18

47

Views

Decomposing $(x^2-y,z-1)$ into primary ideals

Published on 29 Mar 2026 - 15:03

score 286 · Answer 12 · 2026-03-25 03:02:36

286

Views

Question about the integral closure of adjoining a square root to a UFD?

Published on 25 Mar 2026 - 3:02

score 140 · Answer 13 · 2026-03-25 23:42:35

140

Views

For $m \in \text{max} \ R[X]$ and $f \in R[X] \setminus m, \ R[X]_f$ is not a local ring

Published on 25 Mar 2026 - 23:42

score 171 · Answer 14 · 2026-03-28 13:41:59

171

Views

Classification of prime ideals of $\mathbb{Z}[[X]]$

Published on 28 Mar 2026 - 13:41

score 276 · Answer 15 · 2026-03-25 06:01:27

276

Views

Is there a non-artinian noetherian ring whose non-units are zero-divisors?

Published on 25 Mar 2026 - 6:01

List Question

how to prove a graded version of Nakayama's lemma

In a ring with no nilpotent elements (0) is not decomposable.

Is there accepted notation for the homogeneous part of highest degree, and is there a name for "pseudodivision"?

What is $S^{-1}N$ in $S^{-1}M$?

Is the quotient ring $K[x]/\langle f\rangle$ a $n$-dimensional $K$-vector space?

If sum and product of elements are integral, they must be integral

A question about $S^{-1}R\otimes_R M\cong S^{-1}M$ as $S^{-1}R$-modules

Do subrings contain 0, the additive identity because $1-1=0$ in subrings as in subfields?

Minimal prime of a ring is contraction of some prime ideal of any extension of the ring.

Proving an $R$-module isomorphism is in fact an $R/I$-module isomorphism using universal properties.

Decomposing $(x^2-y,z-1)$ into primary ideals

Question about the integral closure of adjoining a square root to a UFD?

For $m \in \text{max} \ R[X]$ and $f \in R[X] \setminus m, \ R[X]_f$ is not a local ring

Classification of prime ideals of $\mathbb{Z}[[X]]$

Is there a non-artinian noetherian ring whose non-units are zero-divisors?

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