Question

Finitely generated R-module is a field iff R is a field?

score 800 · Answer 1 · 2018-08-12 23:44:08

800

Views

Finitely generated R-module is a field iff R is a field?

Published on 12 Aug 2018 - 23:44

score 212 · Answer 2 · 2018-08-13 01:57:23

212

Views

Localization of a finitely generated module is nonzero iff the anihilator is contained in the prime ideal?

Published on 13 Aug 2018 - 1:57

score 50 · Answer 3 · 2026-03-26 16:23:01

50

Views

Example of commutative ring with two elements that don't generate entire ring

Published on 26 Mar 2026 - 16:23

score 239 · Answer 4 · 2026-03-25 07:41:54

239

Views

Noncommutative rings and prime/maximal ideals

Published on 25 Mar 2026 - 7:41

score 152 · Answer 5 · 2018-08-13 14:29:11

152

Views

Does there exist a polynomial it does not have any integer root but has at least one root in $\Bbb Z_n$ , $\forall n \in \Bbb Z$?

Published on 13 Aug 2018 - 14:29

score 405 · Answer 6 · 2018-08-13 16:21:32

405

Views

Prove that there is a nontrivial ring homomorphism from $\mathbb{Q}[x,y]/(x,y)^2$ to $\mathbb{C}$.

Published on 13 Aug 2018 - 16:21

score 154 · Answer 7 · 2018-08-14 03:05:03

154

Views

Ring homomorphism between unital rings

Published on 14 Aug 2018 - 3:05

score 70 · Answer 8 · 2026-03-28 07:43:30

70

Views

Cardinality of generated rings and generated modules

Published on 28 Mar 2026 - 7:43

score 151 · Answer 9 · 2018-08-14 07:02:10

151

Views

Unital rings correspondence by a ring homomorphism

Published on 14 Aug 2018 - 7:02

score 73 · Answer 10 · 2026-03-25 17:26:55

73

Views

What does it mean for a member of formal power series over a field to be algebraic over polynomial ring of that field?

Published on 25 Mar 2026 - 17:26

score 2.1k · Answer 11 · 2018-08-14 13:15:39

2.1k

Views

Every finite commutative ring with no zero divisors contains a multiplicative identity?

Published on 14 Aug 2018 - 13:15

score 125 · Answer 12 · 2026-03-25 04:40:37

125

Views

Finding an explicit map associated with the quotient ring of Gaussian integers

Published on 25 Mar 2026 - 4:40

score 597 · Answer 13 · 2026-03-26 04:16:06

597

Views

How to multiply in the formal Laurent series ring

Published on 26 Mar 2026 - 4:16

score 43 · Answer 14 · 2026-03-29 06:29:02

43

Views

Ideal quotients - when does $I:h^2 = I:h$ hold?

Published on 29 Mar 2026 - 6:29

score 519 · Answer 15 · 2018-08-15 04:36:38

519

Views

Non-unital ring contains a unital ring as a subring?

Published on 15 Aug 2018 - 4:36

List Question

Finitely generated R-module is a field iff R is a field?

Localization of a finitely generated module is nonzero iff the anihilator is contained in the prime ideal?

Example of commutative ring with two elements that don't generate entire ring

Noncommutative rings and prime/maximal ideals

Does there exist a polynomial it does not have any integer root but has at least one root in $\Bbb Z_n$ , $\forall n \in \Bbb Z$?

Prove that there is a nontrivial ring homomorphism from $\mathbb{Q}[x,y]/(x,y)^2$ to $\mathbb{C}$.

Ring homomorphism between unital rings

Cardinality of generated rings and generated modules

Unital rings correspondence by a ring homomorphism

What does it mean for a member of formal power series over a field to be algebraic over polynomial ring of that field?

Every finite commutative ring with no zero divisors contains a multiplicative identity?

Finding an explicit map associated with the quotient ring of Gaussian integers

How to multiply in the formal Laurent series ring

Ideal quotients - when does $I:h^2 = I:h$ hold?

Non-unital ring contains a unital ring as a subring?

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