Question

If $f(x+y) = f(x) + f(y)$, $f(1) = 1$ and for all $x,y$, $f(xy) = f(x)f(y)$ or $f(xy) = f(y)f(x)$, then $f$ is a homomorphism or an anti-homomorphism

score 615 · Answer 1 · 2017-07-08 16:52:38

615

Views

If $f(x+y) = f(x) + f(y)$, $f(1) = 1$ and for all $x,y$, $f(xy) = f(x)f(y)$ or $f(xy) = f(y)f(x)$, then $f$ is a homomorphism or an anti-homomorphism

Published on 08 Jul 2017 - 16:52

score 2.3k · Answer 2 · 2017-07-11 15:16:33

2.3k

Views

Let $I$ and $J$ be ideals of a commutative ring $R$ such that $I + J = R$. Show that there is an ideal $K$ in $R$ with $R/K \cong R/I \times R/J$

Published on 11 Jul 2017 - 15:16

score 1.2k · Answer 3 · 2017-07-16 23:23:19

1.2k

Views

If $R$ is a subring of a field $F$, then the ring of fractions is embedded in $F$

Published on 16 Jul 2017 - 23:23

score 734 · Answer 4 · 2026-03-26 17:36:52

734

Views

On ring isomorphism between cartesian products of rings

Published on 26 Mar 2026 - 17:36

score 403 · Answer 5 · 2017-07-27 15:45:57

403

Views

Injective ring homomorphism between finite direct product of rings

Published on 27 Jul 2017 - 15:45

score 74 · Answer 6 · 2017-07-28 20:46:51

74

Views

When do contractions respect ideal sums?

Published on 28 Jul 2017 - 20:46

score 97 · Answer 7 · 2017-08-17 20:04:21

97

Views

Construct a bijection $\mathrm{Hom}_{\mathbb C}(\mathbb C[x,y]/(xy-1),\mathbb C) \to \mathbb C\setminus \{0\}$

Published on 17 Aug 2017 - 20:04

score 34 · Answer 8 · 2017-08-31 20:32:15

34

Views

Construct a bijection explicitly.

Published on 31 Aug 2017 - 20:32

score 689 · Answer 9 · 2017-09-09 08:34:23

689

Views

Describe all ring homomorphisms from $\mathbb{Z}\times \mathbb{Z}$ into $\mathbb{Z}_7$

Published on 09 Sep 2017 - 8:34

score 1.7k · Answer 10 · 2017-09-15 17:05:53

1.7k

Views

Kernel of the map $\phi :\mathbb{R}[x]\to\mathbb{C}$ defined by $f(x)\mapsto f(2+i)$

Published on 15 Sep 2017 - 17:05

score 6.5k · Answer 11 · 2017-09-23 01:41:17

6.5k

Views

What is an evaluation map in ring theory?

Published on 23 Sep 2017 - 1:41

score 401 · Answer 12 · 2017-09-24 00:26:38

401

Views

Prove $Ker(\phi) = (13,i-5)$ and $Ker(\phi)$ is a principal ideal.

Published on 24 Sep 2017 - 0:26

score 654 · Answer 13 · 2017-09-24 01:44:21

654

Views

Relation between the kernel of two ring homomorphisms

Published on 24 Sep 2017 - 1:44

score 144 · Answer 14 · 2017-09-26 16:39:32

144

Views

Bijection between homomorphisms $\mathbb Z[i]\to R$ and set $x\in R$ with $x^2+1=0$

Published on 26 Sep 2017 - 16:39

score 112 · Answer 15 · 2017-09-26 17:12:03

112

Views

Abstract Algebra, homomorphism of rings, and equivalence classes.

Published on 26 Sep 2017 - 17:12

List Question

If $f(x+y) = f(x) + f(y)$, $f(1) = 1$ and for all $x,y$, $f(xy) = f(x)f(y)$ or $f(xy) = f(y)f(x)$, then $f$ is a homomorphism or an anti-homomorphism

Let $I$ and $J$ be ideals of a commutative ring $R$ such that $I + J = R$. Show that there is an ideal $K$ in $R$ with $R/K \cong R/I \times R/J$

If $R$ is a subring of a field $F$, then the ring of fractions is embedded in $F$

On ring isomorphism between cartesian products of rings

Injective ring homomorphism between finite direct product of rings

When do contractions respect ideal sums?

Construct a bijection $\mathrm{Hom}_{\mathbb C}(\mathbb C[x,y]/(xy-1),\mathbb C) \to \mathbb C\setminus \{0\}$

Construct a bijection explicitly.

Describe all ring homomorphisms from $\mathbb{Z}\times \mathbb{Z}$ into $\mathbb{Z}_7$

Kernel of the map $\phi :\mathbb{R}[x]\to\mathbb{C}$ defined by $f(x)\mapsto f(2+i)$

What is an evaluation map in ring theory?

Prove $Ker(\phi) = (13,i-5)$ and $Ker(\phi)$ is a principal ideal.

Relation between the kernel of two ring homomorphisms

Bijection between homomorphisms $\mathbb Z[i]\to R$ and set $x\in R$ with $x^2+1=0$

Abstract Algebra, homomorphism of rings, and equivalence classes.

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