Question

For a ring homomorphism prove that $f(a^{-1})=[f(a)]^{-1}$

score 657 · Answer 1 · 2026-03-25 06:05:10

For a ring homomorphism prove that $f(a^{-1})=[f(a)]^{-1}$

Published on 25 Mar 2026 - 6:05

score 105 · Answer 2 · 2018-11-05 23:03:19

let R be the ring of linear transformations under V where $\dim_{D} (V) = \infty $ show that $R$ is left primitive but it is not simple

score 51 · Answer 3 · 2026-03-26 19:01:47

51

Views

Find a content of $(1 + w)x^4 + ( -1 + 2w )x^3 + (1-2w )x^2 + 3x + (2 + 3w ) \in \mathbb{Z}[w][x]$

Published on 26 Mar 2026 - 19:01

score 736 · Answer 4 · 2026-03-26 02:57:47

736

Views

Let $F$ be a field, when is the quotient ring $F[x]/(x^2+1)F[x]$ an integral domain?

Published on 26 Mar 2026 - 2:57

score 281 · Answer 5 · 2026-03-29 22:14:33

281

Views

Prove that a commutative right primitive ring is a field

Published on 29 Mar 2026 - 22:14

score 65 · Answer 6 · 2026-03-25 19:01:16

65

Views

Relationship between a polynomial and its constant term (ring)

Published on 25 Mar 2026 - 19:01

score 51 · Answer 7 · 2026-04-02 05:23:42

51

Views

Which are the positive integers $ r $ such that $\mathbb{Z}^{r} $ can be endowed with a structure of UFD?

Published on 02 Apr 2026 - 5:23

score 79 · Answer 8 · 2026-03-25 03:00:58

79

Views

Visualization of quadratic rings $\mathbb{Z}[\sqrt{d}]$

Published on 25 Mar 2026 - 3:00

score 36 · Answer 9 · 2026-03-25 01:22:20

36

Views

Analogue for Group Rings for multiplicative sets

Published on 25 Mar 2026 - 1:22

score 463 · Answer 10 · 2026-03-25 12:37:37

463

Views

Proving that $\mathbb{Z}/128\mathbb{Z}$ has exactly one maximal ideal?

Published on 25 Mar 2026 - 12:37

score 395 · Answer 11 · 2026-03-25 03:00:38

395

Views

Graphical multiplication tables for $\mathbb{Z}/p\mathbb{Z}$ and $\mathbb{Z}$

Published on 25 Mar 2026 - 3:00

score 2.4k · Answer 12 · 2026-03-25 04:39:28

2.4k

Views

What is an inclusion in a ring homomorphism?

Published on 25 Mar 2026 - 4:39

score 91 · Answer 13 · 2018-11-07 21:08:49

91

Views

Showing that a function between $\Bbb R[x]/(x^2 - 1)$ and $ \Bbb R\times \Bbb R $ is surjective?

Published on 07 Nov 2018 - 21:08

score 46 · Answer 14 · 2026-03-26 02:56:23

46

Views

Prove that $f$ or $g$ is reducible given that $\{rf+sg:r,s\in F[x]\} = N$ is a proper ideal and $\deg f \neq \deg g$.

Published on 26 Mar 2026 - 2:56

score 636 · Answer 15 · 2026-03-25 17:42:02

636

Views

Showing that if $\Bbb Z/ab\Bbb Z$ is isomorphic to $\Bbb Z/a\Bbb Z \times \Bbb Z/b\Bbb Z$, then $gcd(a,b)=1$ necessarily.

Published on 25 Mar 2026 - 17:42

List Question

For a ring homomorphism prove that $f(a^{-1})=[f(a)]^{-1}$

let R be the ring of linear transformations under V where $\dim_{D} (V) = \infty $ show that $R$ is left primitive but it is not simple

Find a content of $(1 + w)x^4 + ( -1 + 2w )x^3 + (1-2w )x^2 + 3x + (2 + 3w ) \in \mathbb{Z}[w][x]$

Let $F$ be a field, when is the quotient ring $F[x]/(x^2+1)F[x]$ an integral domain?

Prove that a commutative right primitive ring is a field

Relationship between a polynomial and its constant term (ring)

Which are the positive integers $ r $ such that $\mathbb{Z}^{r} $ can be endowed with a structure of UFD?

Visualization of quadratic rings $\mathbb{Z}[\sqrt{d}]$

Analogue for Group Rings for multiplicative sets

Proving that $\mathbb{Z}/128\mathbb{Z}$ has exactly one maximal ideal?

Graphical multiplication tables for $\mathbb{Z}/p\mathbb{Z}$ and $\mathbb{Z}$

What is an inclusion in a ring homomorphism?

Showing that a function between $\Bbb R[x]/(x^2 - 1)$ and $ \Bbb R\times \Bbb R $ is surjective?

Prove that $f$ or $g$ is reducible given that $\{rf+sg:r,s\in F[x]\} = N$ is a proper ideal and $\deg f \neq \deg g$.

Showing that if $\Bbb Z/ab\Bbb Z$ is isomorphic to $\Bbb Z/a\Bbb Z \times \Bbb Z/b\Bbb Z$, then $gcd(a,b)=1$ necessarily.

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