Question

Jacobson radical = nilradical iff every open set of $\text{Spec}A$ contains a closed point.

score 657 · Answer 1 · 2026-03-17 16:58:08

657

Views

Jacobson radical = nilradical iff every open set of $\text{Spec}A$ contains a closed point.

Published on 17 Mar 2026 - 16:58

score 190 · Answer 2 · 2026-03-17 06:19:57

190

Views

A commutative ring is prime if and only if it is a domain.

Published on 17 Mar 2026 - 6:19

score 247 · Answer 3 · 2026-03-22 12:54:56

247

Views

Find gcd and invertible elements of a ring.

Published on 22 Mar 2026 - 12:54

score 15.9k · Answer 4 · 2026-03-24 01:55:52

15.9k

Views

Prove that $R[x]$ is an integral domain if and only if $R$ is an integral domain.

Published on 24 Mar 2026 - 1:55

score 186 · Answer 5 · 2026-03-20 04:20:30

186

Views

Prove that $Z[i]/(5)$ is not a field. Check proof?

Published on 20 Mar 2026 - 4:20

score 150 · Answer 6 · 2026-03-17 14:06:15

150

Views

If $P$ is a prime ideal of $R[x;\delta]$ such as $P\cap R=\{0\}$, is $P(Q[x;\delta])$ also prime?

Published on 17 Mar 2026 - 14:06

score 435 · Answer 7 · 2026-03-20 11:18:53

435

Views

Let $R$ be a simple ring having a minimal left ideal $L$. Then every simple $R$-module is isomorphic to $L$.

Published on 20 Mar 2026 - 11:18

score 409 · Answer 8 · 2026-03-22 09:35:02

409

Views

A quotient of a polynomial ring

Published on 22 Mar 2026 - 9:35

score 38 · Answer 9 · 2026-03-20 01:46:06

38

Views

Does a ring isomorphism between two $F$-algebras must be a $F$-linear transformation

Published on 20 Mar 2026 - 1:46

score 346 · Answer 10 · 2026-03-20 05:03:36

346

Views

Prove that a ring of fractions is a local ring

Published on 20 Mar 2026 - 5:03

score 91 · Answer 11 · 2026-03-19 22:02:14

91

Views

A question about Maschke theorem

Published on 19 Mar 2026 - 22:02

score 150 · Answer 12 · 2026-03-19 20:34:59

150

Views

Let $L$ be a left ideal of a ring R such that $ RL \neq 0$. Then $L$ is simple as an R-module if and only if $L$ is a minimal left ideal?

Published on 19 Mar 2026 - 20:34

score 331 · Answer 13 · 2026-03-22 12:59:30

331

Views

The ring $\mathrm{End}_D(V) $ is simple if $V$ is finite dimensional.

Published on 22 Mar 2026 - 12:59

score 872 · Answer 14 · 2026-03-17 21:22:42

872

Views

Show $\varphi:R/I\to R/J$ is a well-defined ring homomorphism

Published on 17 Mar 2026 - 21:22

score 129 · Answer 15 · 2026-03-24 10:13:39

129

Views

Tensor product $M\otimes_B Hom_B(M,B)$ equals $End_B(M)$, $M$ finitely generated over $B$ and projective

Published on 24 Mar 2026 - 10:13

List Question

Jacobson radical = nilradical iff every open set of $\text{Spec}A$ contains a closed point.

A commutative ring is prime if and only if it is a domain.

Find gcd and invertible elements of a ring.

Prove that $R[x]$ is an integral domain if and only if $R$ is an integral domain.

Prove that $Z[i]/(5)$ is not a field. Check proof?

If $P$ is a prime ideal of $R[x;\delta]$ such as $P\cap R=\{0\}$, is $P(Q[x;\delta])$ also prime?

Let $R$ be a simple ring having a minimal left ideal $L$. Then every simple $R$-module is isomorphic to $L$.

A quotient of a polynomial ring

Does a ring isomorphism between two $F$-algebras must be a $F$-linear transformation

Prove that a ring of fractions is a local ring

A question about Maschke theorem

Let $L$ be a left ideal of a ring R such that $ RL \neq 0$. Then $L$ is simple as an R-module if and only if $L$ is a minimal left ideal?

The ring $\mathrm{End}_D(V) $ is simple if $V$ is finite dimensional.

Show $\varphi:R/I\to R/J$ is a well-defined ring homomorphism

Tensor product $M\otimes_B Hom_B(M,B)$ equals $End_B(M)$, $M$ finitely generated over $B$ and projective

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