Let $P$ and $Q$ are distinct prime ideals of the ring $R$ with $P \cap Q = 0$, then $R$ is isomorphic to a subring of the direct product of two fields

score 114 · Answer 7 · 2026-03-26 12:06:40

114

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homomorphisms from a (semi)local ring to a ring with infinitely many maximal ideals

Published on 26 Mar 2026 - 12:06

score 81 · Answer 8 · 2024-01-14 15:00:12

81

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Construct maximal ideal in multivariate polynomial ring

Published on 14 Jan 2024 - 15:00

score 15 · Answer 9 · 2026-03-04 22:58:37

15

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Noncommutative Nakayama's Lemma for Maximal Ideal Inclusion

Published on 04 Mar 2026 - 22:58

score 51 · Answer 10 · 2026-03-25 21:48:17

51

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Dominating rings: $\mathfrak{m}_A=A\cap \mathfrak{m}_B\Longleftrightarrow \mathfrak{m}_A\subset \mathfrak{m}_B$

Published on 25 Mar 2026 - 21:48

score 112 · Answer 11 · 2024-01-31 13:54:30

112

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In a commutative unity ring $R$, if $M$ is a maximal ideal then ring $R/M^n$ has only one prime ideal

Published on 31 Jan 2024 - 13:54

score 72 · Answer 12 · 2024-02-01 19:49:44

72

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Rings of continuous functions

Published on 01 Feb 2024 - 19:49

score 119 · Answer 13 · 2026-03-26 01:11:05

119

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Small generating set for the unique minimal prime ideal of a finitely generated $\mathbb{C}$-algebra

Published on 26 Mar 2026 - 1:11

score 93 · Answer 14 · 2024-02-02 11:05:51

93

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Is a prime/maximal ideal in the fraction ring prime/maximal in the underlying ring?

Published on 02 Feb 2024 - 11:05

score 107 · Answer 15 · 2026-03-27 05:38:57

107

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Let $R$ be a Noetherian commutative ring with zero nilradical and with any localization at a maximal ideal as a finite ring. Prove that $R$ is finite

Published on 27 Mar 2026 - 5:38

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