Question

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

score 669 · Answer 1 · 2026-05-07 12:50:02

669

Views

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

Published on 07 May 2026 - 12:50

score 202 · Answer 2 · 2026-05-06 09:10:06

202

Views

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

Published on 06 May 2026 - 9:10

score 266 · Answer 3 · 2026-05-06 06:44:01

266

Views

Find gcd and invertible elements of a ring.

Published on 06 May 2026 - 6:44

score 15.9k · Answer 4 · 2026-05-07 12:50:24

15.9k

Views

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

Published on 07 May 2026 - 12:50

score 199 · Answer 5 · 2026-05-02 20:17:01

199

Views

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

Published on 02 May 2026 - 20:17

score 158 · Answer 6 · 2026-05-05 03:47:31

158

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 05 May 2026 - 3:47

score 447 · Answer 7 · 2026-05-02 18:26:56

447

Views

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

Published on 02 May 2026 - 18:26

score 416 · Answer 8 · 2026-04-29 12:23:41

416

Views

A quotient of a polynomial ring

Published on 29 Apr 2026 - 12:23

score 47 · Answer 9 · 2026-05-02 18:45:00

47

Views

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

Published on 02 May 2026 - 18:45

score 353 · Answer 10 · 2026-04-29 12:23:50

353

Views

Prove that a ring of fractions is a local ring

Published on 29 Apr 2026 - 12:23

score 98 · Answer 11 · 2026-04-29 12:23:41

98

Views

A question about Maschke theorem

Published on 29 Apr 2026 - 12:23

score 157 · Answer 12 · 2026-05-05 07:46:00

157

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 05 May 2026 - 7:46

score 339 · Answer 13 · 2026-05-10 09:42:55

339

Views

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

Published on 10 May 2026 - 9:42

score 885 · Answer 14 · 2026-05-05 04:06:26

885

Views

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

Published on 05 May 2026 - 4:06

score 139 · Answer 15 · 2026-04-29 12:23:45

139

Views

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

Published on 29 Apr 2026 - 12:23

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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