Question

Can we control the number of homogeneous generators of a f.g. homogeneous ideal?

score 193 · Answer 1 · 2020-03-12 00:37:38

193

Views

Can we control the number of homogeneous generators of a f.g. homogeneous ideal?

Published on 12 Mar 2020 - 0:37

score 108 · Answer 2 · 2026-03-07 10:59:57

108

Views

$M$ is a coherent left $R$-module implies $M/IM$ is a coherent $R/I$-module.

Published on 07 Mar 2026 - 10:59

score 103 · Answer 3 · 2026-03-23 00:37:22

103

Views

$I$ finitely presented nilpotent ideal of a commutative ring $R$ and $R/I$ coherent implies $R$ coherent

Published on 23 Mar 2026 - 0:37

score 134 · Answer 4 · 2026-03-25 02:02:50

134

Views

Coherent Ring, whose nilradical is not finitely generated.

Published on 25 Mar 2026 - 2:02

score 84 · Answer 5 · 2023-11-11 13:18:24

84

Views

Rings where finitely generated ideals are closed under countable intersection

Published on 11 Nov 2023 - 13:18

score 27 · Answer 6 · 2026-03-15 06:35:33

27

Views

Is a Noetherian sheaf of rings stalkwise Noetherian?

Published on 15 Mar 2026 - 6:35

score 67 · Answer 7 · 2026-03-25 05:59:43

67

Views

Is a commutative perfect and coherent ring an Artin ring?

Published on 25 Mar 2026 - 5:59

score 342 · Answer 8 · 2015-10-12 10:30:45

342

Views

Geometric intuition for coherent rings, modules, and sheaves

Published on 12 Oct 2015 - 10:30

score 1k · Answer 9 · 2026-03-09 16:29:13

1k

Views

Is every ring/module the filtered colimit of its finitely presented/coherent/quasicoherent subrings/submodules?

Published on 09 Mar 2026 - 16:29

score 102 · Answer 10 · 2015-11-22 16:05:18

102

Views

(quasi)coherent rings for which $\dim R[T]\neq \dim R+1$

Published on 22 Nov 2015 - 16:05

score 1.3k · Answer 11 · 2016-03-02 14:41:07

1.3k

Views

Polynomial ring in infinitely many variables over a noetherian ring is coherent

Published on 02 Mar 2016 - 14:41

score 87 · Answer 12 · 2026-03-14 13:11:42

87

Views

infinite indeterminates over a left noetherian ring is left coherent(want a basic proof)

Published on 14 Mar 2026 - 13:11

score 65 · Answer 13 · 2018-01-01 16:06:38

65

Views

Do two similar boolean matrices have same number of non-zero entries?

Published on 01 Jan 2018 - 16:06

score 266 · Answer 14 · 2026-03-24 19:21:42

266

Views

Infinite intersection of finitely generated ideals in a coherent ring.

Published on 24 Mar 2026 - 19:21

score 107 · Answer 15 · 2026-03-25 02:41:40

107

Views

Are coherent modules hopfian?

Published on 25 Mar 2026 - 2:41

List Question

Can we control the number of homogeneous generators of a f.g. homogeneous ideal?

$M$ is a coherent left $R$-module implies $M/IM$ is a coherent $R/I$-module.

$I$ finitely presented nilpotent ideal of a commutative ring $R$ and $R/I$ coherent implies $R$ coherent

Coherent Ring, whose nilradical is not finitely generated.

Rings where finitely generated ideals are closed under countable intersection

Is a Noetherian sheaf of rings stalkwise Noetherian?

Is a commutative perfect and coherent ring an Artin ring?

Geometric intuition for coherent rings, modules, and sheaves

Is every ring/module the filtered colimit of its finitely presented/coherent/quasicoherent subrings/submodules?

(quasi)coherent rings for which $\dim R[T]\neq \dim R+1$

Polynomial ring in infinitely many variables over a noetherian ring is coherent

infinite indeterminates over a left noetherian ring is left coherent(want a basic proof)

Do two similar boolean matrices have same number of non-zero entries?

Infinite intersection of finitely generated ideals in a coherent ring.

Are coherent modules hopfian?

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