Question

For ring homomorphism $\phi:R\to S$, prove that $\phi$ is an isomorphism iff $\phi$ is onto and $ker(\phi)=\left \{0_{R} \right \}$.

score 2.5k · Answer 1 · 2026-04-22 16:25:03

2.5k

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For ring homomorphism $\phi:R\to S$, prove that $\phi$ is an isomorphism iff $\phi$ is onto and $ker(\phi)=\left \{0_{R} \right \}$.

Published on 22 Apr 2026 - 16:25

score 4.4k · Answer 2 · 2026-04-11 22:30:53

4.4k

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Is a nonsingular matrix not the same as an invertible matrix?

Published on 11 Apr 2026 - 22:30

score 2.2k · Answer 3 · 2026-04-13 22:18:11

2.2k

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Published on 13 Apr 2026 - 22:18

score 167 · Answer 4 · 2026-04-15 11:27:47

167

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Published on 15 Apr 2026 - 11:27

score 560 · Answer 5 · 2026-04-13 06:09:24

560

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score 590 · Answer 6 · 2026-05-04 12:31:23

590

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score 992 · Answer 7 · 2026-04-12 05:05:02

992

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Published on 12 Apr 2026 - 5:05

score 54 · Answer 8 · 2026-04-17 09:31:48

54

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Let $A = \{ 2, 5, 9\}$. Let $K = \{ F ∈ S_9 | F(a) = a, ∀a ∈ A \}$. Determine order of $K$.

Published on 17 Apr 2026 - 9:31

score 182 · Answer 9 · 2026-04-14 00:54:12

182

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Shorter proof that $\mathbb{C}\otimes_{\mathbb{R}} \mathbb{C}\cong \mathbb{C}^2$

Published on 14 Apr 2026 - 0:54

score 390 · Answer 10 · 2026-04-23 03:08:48

390

Views

Intro to computational "side effects" from an algebraic perspective.

Published on 23 Apr 2026 - 3:08

score 1.9k · Answer 11 · 2026-04-16 12:40:54

1.9k

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Show that $\Bbb F_2[x]/(x^3+x+1)$ is a field and more...

Published on 16 Apr 2026 - 12:40

score 87 · Answer 12 · 2026-04-15 03:58:30

87

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Published on 15 Apr 2026 - 3:58

score 267 · Answer 13 · 2026-04-29 12:46:23

267

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Published on 29 Apr 2026 - 12:46

score 392 · Answer 14 · 2026-04-23 00:06:18

392

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Torsion subgroup of $\mathbb{Z}\times \left( \mathbb{Z}/n\mathbb{Z}\right)$

Published on 23 Apr 2026 - 0:06

score 1.4k · Answer 15 · 2026-04-11 23:11:00

1.4k

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Published on 11 Apr 2026 - 23:11

List Question

For ring homomorphism $\phi:R\to S$, prove that $\phi$ is an isomorphism iff $\phi$ is onto and $ker(\phi)=\left \{0_{R} \right \}$.

Is a nonsingular matrix not the same as an invertible matrix?

Field and algebraic extension. How to prove that $[K: F]$ is finite?

Solving matrix equations (or systems of linear equations) over $\mathbb Z$

Tensor product, injective homomorphism

How to understand the coidea of a colagebra?

One-dimensional representations of $GL(n,K)$

Let $A = \{ 2, 5, 9\}$. Let $K = \{ F ∈ S_9 | F(a) = a, ∀a ∈ A \}$. Determine order of $K$.

Shorter proof that $\mathbb{C}\otimes_{\mathbb{R}} \mathbb{C}\cong \mathbb{C}^2$

Intro to computational "side effects" from an algebraic perspective.

Show that $\Bbb F_2[x]/(x^3+x+1)$ is a field and more...

Find a generator of the intersection of three subgroups of the integers

How many $n$-digit automorphic (circular) numbers are there?

Torsion subgroup of $\mathbb{Z}\times \left( \mathbb{Z}/n\mathbb{Z}\right)$

Applications of the strong Cayley theorem

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