Question

Can ring homomorphisms be characterized as ring maps such that preimage of any ideal is an ideal?

score 708 · Answer 1 · 2026-04-13 02:27:36

708

Views

Can ring homomorphisms be characterized as ring maps such that preimage of any ideal is an ideal?

Published on 13 Apr 2026 - 2:27

score 769 · Answer 2 · 2026-04-09 16:54:38

769

Views

Definition of Module Structure Induced by Ring Homomorphism

Published on 09 Apr 2026 - 16:54

score 85 · Answer 3 · 2026-04-11 07:52:34

85

Views

How do I verify if $\phi : \mathbb{Z}_{6} \rightarrow \mathbb{Z}_{36}$ is well-defined?

Published on 11 Apr 2026 - 7:52

score 90 · Answer 4 · 2026-04-30 12:37:13

90

Views

Substitution on $\mathbb{R}$ as isomorphisms

Published on 30 Apr 2026 - 12:37

score 1.9k · Answer 5 · 2026-04-14 19:36:23

1.9k

Views

For ring homomorphism $\phi:R\to S$, prove that $\phi(R)$ is a subring of $S$.

Published on 14 Apr 2026 - 19:36

score 2.8k · Answer 6 · 2026-04-15 16:40:34

2.8k

Views

For ring homomorphism $\phi:R\to S$, prove that if $R$ is a field and $\phi(R)\neq \left \{0_{S} \right \}$, then $\phi(R)$ is a field.

Published on 15 Apr 2026 - 16:40

score 2.5k · Answer 7 · 2026-04-22 16:25:03

2.5k

Views

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 35 · Answer 8 · 2026-04-14 21:56:17

35

Views

$k$ be an algebraically closed field , $R=M(n,k)$ , then $k \cong End_R (k^n)$

Published on 14 Apr 2026 - 21:56

score 3.3k · Answer 9 · 2026-04-16 16:22:21

3.3k

Views

Find all homomorphisms $\phi: \Bbb{Z}/6\Bbb{Z} \to \Bbb{Z}/15\Bbb{Z}$.

Published on 16 Apr 2026 - 16:22

score 129 · Answer 10 · 2026-04-16 12:51:58

129

Views

On the kernel of the surjective ring homomorphism $R[X] \to R[ab^{-1}]$ taking $X$ to $ab^{-1}$

Published on 16 Apr 2026 - 12:51

score 144 · Answer 11 · 2026-04-12 11:49:51

144

Views

Proving that $D^{-1}\mathbb{Z}\cong \mathbb{Z}[x]/(px-1)$

Published on 12 Apr 2026 - 11:49

score 1.1k · Answer 12 · 2026-04-15 12:59:13

1.1k

Views

Example of non surjective ring homomorphisim where im$(\phi)$ is not an ideal

Published on 15 Apr 2026 - 12:59

score 62 · Answer 13 · 2026-04-13 04:08:28

62

Views

Proof this factor ring is field.

Published on 13 Apr 2026 - 4:08

score 378 · Answer 14 · 2026-04-15 20:20:12

378

Views

Basis for $R[x]/(f)$ as an $R$-module

Published on 15 Apr 2026 - 20:20

score 82 · Answer 15 · 2026-04-15 06:12:12

82

Views

Show that the ring homomorphism $\phi:R\to R/I$ defined by $\phi(r)=r+I$ is well-defined.

Published on 15 Apr 2026 - 6:12

List Question

Can ring homomorphisms be characterized as ring maps such that preimage of any ideal is an ideal?

Definition of Module Structure Induced by Ring Homomorphism

How do I verify if $\phi : \mathbb{Z}_{6} \rightarrow \mathbb{Z}_{36}$ is well-defined?

Substitution on $\mathbb{R}$ as isomorphisms

For ring homomorphism $\phi:R\to S$, prove that $\phi(R)$ is a subring of $S$.

For ring homomorphism $\phi:R\to S$, prove that if $R$ is a field and $\phi(R)\neq \left \{0_{S} \right \}$, then $\phi(R)$ is a field.

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

$k$ be an algebraically closed field , $R=M(n,k)$ , then $k \cong End_R (k^n)$

Find all homomorphisms $\phi: \Bbb{Z}/6\Bbb{Z} \to \Bbb{Z}/15\Bbb{Z}$.

On the kernel of the surjective ring homomorphism $R[X] \to R[ab^{-1}]$ taking $X$ to $ab^{-1}$

Proving that $D^{-1}\mathbb{Z}\cong \mathbb{Z}[x]/(px-1)$

Example of non surjective ring homomorphisim where im$(\phi)$ is not an ideal

Proof this factor ring is field.

Basis for $R[x]/(f)$ as an $R$-module

Show that the ring homomorphism $\phi:R\to R/I$ defined by $\phi(r)=r+I$ is well-defined.

Trending Questions

Popular # Hahtags

Popular Questions