Question

Prove that the homomorphism $\phi:R\to S^{-1}R$ is injective if and only if $S$ contains no zero-divisors.

score 414 · Answer 1 · 2026-03-20 06:35:36

414

Views

Prove that the homomorphism $\phi:R\to S^{-1}R$ is injective if and only if $S$ contains no zero-divisors.

Published on 20 Mar 2026 - 6:35

score 266 · Answer 2 · 2026-03-19 16:27:01

266

Views

Units of $\mathbb{Z}[\omega]$ where $\omega = \frac{1}{2} (1+ \sqrt{a})$, $a<0$ a square free integer.

Published on 19 Mar 2026 - 16:27

score 664 · Answer 3 · 2018-01-28 17:33:19

664

Views

Discrete subrings of $\mathbb R$

Published on 28 Jan 2018 - 17:33

score 66 · Answer 4 · 2018-01-28 18:44:39

66

Views

Understanding elements of $\mathbb Z[\sqrt p+ \sqrt q]$

Published on 28 Jan 2018 - 18:44

score 105 · Answer 5 · 2026-03-20 06:39:03

105

Views

Lying over properties with integral extensions of rings

Published on 20 Mar 2026 - 6:39

score 1.6k · Answer 6 · 2026-03-17 23:39:59

1.6k

Views

Are all prime ideals in a Dedekind domain also principal ideals?

Published on 17 Mar 2026 - 23:39

score 940 · Answer 7 · 2026-03-23 02:17:10

940

Views

What is the correct notion of unique factorization in a ring?

Published on 23 Mar 2026 - 2:17

score 2.2k · Answer 8 · 2018-01-29 08:03:44

2.2k

Views

Algebra - Prove this is a Ring

Published on 29 Jan 2018 - 8:03

score 359 · Answer 9 · 2018-01-29 15:26:53

359

Views

Flatness criterion: If $K$ is any submodule of a finitely generated free module, then $A \otimes_R K \to A \otimes F$ is injective.

Published on 29 Jan 2018 - 15:26

score 372 · Answer 10 · 2018-01-29 21:06:14

372

Views

$\exists x \in R$ and $\exists n \in\mathbb{N}$ such that $x^{n+1} = x^n \implies x^2 = x$

Published on 29 Jan 2018 - 21:06

score 92 · Answer 11 · 2026-03-25 07:15:12

92

Views

Sum of polynomial ideals + intersection with vector spaces

Published on 25 Mar 2026 - 7:15

score 435 · Answer 12 · 2026-03-23 15:44:21

435

Views

Find the ideals of $S^{-1}R$

Published on 23 Mar 2026 - 15:44

score 551 · Answer 13 · 2026-03-24 15:52:48

551

Views

Find all surjective ring homomorphisms $\phi:\mathbb{R}[x] \rightarrow \mathbb{R}.$

Published on 24 Mar 2026 - 15:52

score 362 · Answer 14 · 2026-03-20 03:13:37

362

Views

Is this true? An element which is not contained in a maximal ideal.

Published on 20 Mar 2026 - 3:13

score 31 · Answer 15 · 2018-01-30 16:10:13

31

Views

Question regarding field

Published on 30 Jan 2018 - 16:10

List Question

Prove that the homomorphism $\phi:R\to S^{-1}R$ is injective if and only if $S$ contains no zero-divisors.

Units of $\mathbb{Z}[\omega]$ where $\omega = \frac{1}{2} (1+ \sqrt{a})$, $a<0$ a square free integer.

Discrete subrings of $\mathbb R$

Understanding elements of $\mathbb Z[\sqrt p+ \sqrt q]$

Lying over properties with integral extensions of rings

Are all prime ideals in a Dedekind domain also principal ideals?

What is the correct notion of unique factorization in a ring?

Algebra - Prove this is a Ring

Flatness criterion: If $K$ is any submodule of a finitely generated free module, then $A \otimes_R K \to A \otimes F$ is injective.

$\exists x \in R$ and $\exists n \in\mathbb{N}$ such that $x^{n+1} = x^n \implies x^2 = x$

Sum of polynomial ideals + intersection with vector spaces

Find the ideals of $S^{-1}R$

Find all surjective ring homomorphisms $\phi:\mathbb{R}[x] \rightarrow \mathbb{R}.$

Is this true? An element which is not contained in a maximal ideal.

Question regarding field

Trending Questions

Popular # Hahtags

Popular Questions