Question

Ring homomorphism between quotients of rings of polynomials in many variables

score 112 · Answer 1 · 2026-04-15 02:03:15

112

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Ring homomorphism between quotients of rings of polynomials in many variables

Published on 15 Apr 2026 - 2:03

score 19 · Answer 2 · 2026-04-16 12:51:35

19

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How to prove that $ F[x,x^{-1},y,z]/(z^2-xy)\cong F[x,x^{-1}]\otimes_F\left(F[y,z]\big{/}(z^2-y)\right)$?

Published on 16 Apr 2026 - 12:51

score 26 · Answer 3 · 2026-04-16 02:53:02

26

Views

Proving Primes in an UFD

Published on 16 Apr 2026 - 2:53

score 110 · Answer 4 · 2026-05-11 00:53:25

110

Views

Adjoint action on idempotents in Clifford algebras

Published on 11 May 2026 - 0:53

score 1.2k · Answer 5 · 2026-05-10 14:49:17

1.2k

Views

If $R$ is a PID, $S$ an integral domain and $f: R \to S$ is an epimorphism, why is it that either $f$ is an isomorphism or $S$ is a field?

Published on 10 May 2026 - 14:49

score 49 · Answer 6 · 2026-04-12 09:58:14

Prove that $2x$ is irreducible, but not prime in the ring of polynomials whose all coefficients, excepting the constant term, are even numbers.

score 72 · Answer 7 · 2026-04-14 10:48:45

72

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Factors in a addition modulo p ring

Published on 14 Apr 2026 - 10:48

score 94 · Answer 8 · 2026-04-16 12:22:42

94

Views

Is there any difference between a maximal regular left ideal and a regular maximal left ideal?

Published on 16 Apr 2026 - 12:22

score 475 · Answer 9 · 2026-04-30 03:00:10

475

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Let $ϕ: R → S$ be a ring homomorphism, where $S$ is a domain. Prove that if $u ∈ R$ is nilpotent then $u ∈ \ker ϕ$.

Published on 30 Apr 2026 - 3:00

score 37 · Answer 10 · 2026-04-16 13:05:00

37

Views

$T_1^{n+1}-T_2^{n}$ is prime for $n\in\mathbb{N}$.

Published on 16 Apr 2026 - 13:05

score 239 · Answer 11 · 2026-05-10 14:49:43

239

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$R$ is a commutative ring with $1$, prove that there exist epimorphism from $R[x]$ onto $R$.

Published on 10 May 2026 - 14:49

score 69 · Answer 12 · 2026-04-19 08:13:39

69

Views

What can be said about $ \hat{\otimes}_R:f\otimes g\mapsto f\otimes_R g$?

Published on 19 Apr 2026 - 8:13

score 490 · Answer 13 · 2026-04-16 21:37:29

490

Views

If krull dimension is $0$, then all prime ideals are maximal?

Published on 16 Apr 2026 - 21:37

score 78 · Answer 14 · 2026-03-26 04:14:06

78

Views

Left ideals contain a non-zero idempotent

Published on 26 Mar 2026 - 4:14

score 108 · Answer 15 · 2026-04-25 20:01:57

108

Views

Colimit of the functor $\mathcal{I} \to Rings$

Published on 25 Apr 2026 - 20:01

List Question

Ring homomorphism between quotients of rings of polynomials in many variables

How to prove that $ F[x,x^{-1},y,z]/(z^2-xy)\cong F[x,x^{-1}]\otimes_F\left(F[y,z]\big{/}(z^2-y)\right)$?

Proving Primes in an UFD

Adjoint action on idempotents in Clifford algebras

If $R$ is a PID, $S$ an integral domain and $f: R \to S$ is an epimorphism, why is it that either $f$ is an isomorphism or $S$ is a field?

Prove that $2x$ is irreducible, but not prime in the ring of polynomials whose all coefficients, excepting the constant term, are even numbers.

Factors in a addition modulo p ring

Is there any difference between a maximal regular left ideal and a regular maximal left ideal?

Let $ϕ: R → S$ be a ring homomorphism, where $S$ is a domain. Prove that if $u ∈ R$ is nilpotent then $u ∈ \ker ϕ$.

$T_1^{n+1}-T_2^{n}$ is prime for $n\in\mathbb{N}$.

$R$ is a commutative ring with $1$, prove that there exist epimorphism from $R[x]$ onto $R$.

What can be said about $ \hat{\otimes}_R:f\otimes g\mapsto f\otimes_R g$?

If krull dimension is $0$, then all prime ideals are maximal?

Left ideals contain a non-zero idempotent

Colimit of the functor $\mathcal{I} \to Rings$

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