Question

Show the polynomial $p(x,y) =y^3+xy^2+(x^2+x)y+(4x^3+2x)$ is irreducible in $\mathbb{Z}[x, y]$

score 250 · Answer 1 · 2026-03-25 01:40:03

250

Views

Show the polynomial $p(x,y) =y^3+xy^2+(x^2+x)y+(4x^3+2x)$ is irreducible in $\mathbb{Z}[x, y]$

Published on 25 Mar 2026 - 1:40

score 356 · Answer 2 · 2018-02-24 21:35:19

356

Views

Application of Artin-Wedderburn Theorem to Abelian Group Algebras

Published on 24 Feb 2018 - 21:35

score 105 · Answer 3 · 2026-03-25 17:22:54

105

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Question about irreducible modules and the Artin-Wedderburn Theorem

Published on 25 Mar 2026 - 17:22

score 49 · Answer 4 · 2018-02-25 09:41:17

49

Views

A question about an ideal in power series ring

Published on 25 Feb 2018 - 9:41

score 135 · Answer 5 · 2018-02-25 12:28:48

135

Views

If there is a unital ring homomorphism $f:K\to K'$ between two division rings such then prove that $\text{char}(K)=\text{char}(K').$

Published on 25 Feb 2018 - 12:28

score 68 · Answer 6 · 2018-02-25 13:41:52

Given that $f(x^3)=[f(x)]^3$ for $f:K\to K'$ with $f(x+y)=f(x)+f(y)$, $f(1)=1$ and $K$ and $K'$ two fields with characteristic not equal$2$ and $3$.

score 49 · Answer 7 · 2018-02-25 14:42:06

Let $K$ be a field and $\text{char}(K)=p\not =0.$ Prove that the polynomial $X^{p^n}-a\in K[X]$ for $a\in K$ has at most one root.

score 97 · Answer 8 · 2018-02-25 17:47:00

97

Views

Let $K$ be a division ring and $\text{char}(K)\not = 2$. Show that $x^2+y^2-1$ is irreducible in $K[X,Y].$

Published on 25 Feb 2018 - 17:47

score 361 · Answer 9 · 2018-02-25 18:10:17

361

Views

Minimal ideals in a reduced ring

Published on 25 Feb 2018 - 18:10

score 35 · Answer 10 · 2018-02-25 20:56:49

35

Views

What exactly do normed rings mean intuitively?

Published on 25 Feb 2018 - 20:56

score 600 · Answer 11 · 2018-02-26 00:31:32

600

Views

Proving Ideal in $\mathbb{C}[x, y ,z]$ is Prime

Published on 26 Feb 2018 - 0:31

score 96 · Answer 12 · 2018-02-26 02:33:38

96

Views

Help me understand this proof from Artin's Algebra about algebraic integers in $\mathbb Q[\sqrt d]$.

Published on 26 Feb 2018 - 2:33

score 573 · Answer 13 · 2018-02-26 08:32:51

573

Views

Relation Between Near Ring and Ring

Published on 26 Feb 2018 - 8:32

score 93 · Answer 14 · 2018-02-26 13:27:57

93

Views

Precise definition of $\mathbb{Z}_n[i]$

Published on 26 Feb 2018 - 13:27

score 706 · Answer 15 · 2026-03-25 01:18:26

706

Views

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

Published on 25 Mar 2026 - 1:18

List Question

Show the polynomial $p(x,y) =y^3+xy^2+(x^2+x)y+(4x^3+2x)$ is irreducible in $\mathbb{Z}[x, y]$

Application of Artin-Wedderburn Theorem to Abelian Group Algebras

Question about irreducible modules and the Artin-Wedderburn Theorem

A question about an ideal in power series ring

If there is a unital ring homomorphism $f:K\to K'$ between two division rings such then prove that $\text{char}(K)=\text{char}(K').$

Given that $f(x^3)=[f(x)]^3$ for $f:K\to K'$ with $f(x+y)=f(x)+f(y)$, $f(1)=1$ and $K$ and $K'$ two fields with characteristic not equal$2$ and $3$.

Let $K$ be a field and $\text{char}(K)=p\not =0.$ Prove that the polynomial $X^{p^n}-a\in K[X]$ for $a\in K$ has at most one root.

Let $K$ be a division ring and $\text{char}(K)\not = 2$. Show that $x^2+y^2-1$ is irreducible in $K[X,Y].$

Minimal ideals in a reduced ring

What exactly do normed rings mean intuitively?

Proving Ideal in $\mathbb{C}[x, y ,z]$ is Prime

Help me understand this proof from Artin's Algebra about algebraic integers in $\mathbb Q[\sqrt d]$.

Relation Between Near Ring and Ring

Precise definition of $\mathbb{Z}_n[i]$

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

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