List questions from modules

Published on 25 Mar 2026 - 7:47

64

Views

Is there a name for a module that is simultaneously Hopfian and co-Hopfian?

Published on 30 Oct 2018 - 20:10

357

Views

$K(X)$ is not faithfully flat $K[X]$ module.

Published on 25 Mar 2026 - 6:24

198

Views

Let $R$ be a ring, $M$ an $R$-module, and $A, B ≤ M$ two submodules of $M$ such that $M = A ⊕ B$. Prove that $M/A \cong B$.

Published on 26 Mar 2026 - 19:03

354

Views

Submodule of a semisimple module is just a subsum of decomposition

Published on 31 Oct 2018 - 2:35

56

Views

Is the (truncated) Witt ring an injective module over itself?

Published on 25 Mar 2026 - 9:23

111

Views

Is $\Bbb Z[i]$ flat as $\Bbb Z[2i]$-module?

Published on 25 Mar 2026 - 6:24

262

Views

Divisible module over an integral domain is not projective?

Published on 26 Mar 2026 - 19:37

27

Views

About free modules and finitely generated modules

Published on 03 Nov 2018 - 5:33

81

Views

Prove that $R[X_1,\dots,X_n] \otimes R[Y_1,\dots,Y_m] \cong R[X_1,\dots,X_n,Y_1,\dots Y_m] $

Published on 03 Nov 2018 - 11:00

160

Views

Unitary Ring of Endomorphisms.

Published on 04 Nov 2018 - 4:37

541

Views

Finite index submodules of finitely generated free modules.

Published on 25 Mar 2026 - 5:06

590

Views

length of minimal projective resolution and projective dimension

Published on 27 Feb 2026 - 16:17

114

Views

Is this true: $\operatorname{Hom}_R(S,R) \otimes_S P \cong \operatorname{Hom}_R(P,R)$?

Published on 25 Mar 2026 - 5:10

280

Views

Prove that a commutative right primitive ring is a field

Published on 06 Nov 2018 - 12:27

List Question

Ascending / descending chain condition on graded modules.

Is there a name for a module that is simultaneously Hopfian and co-Hopfian?

$K(X)$ is not faithfully flat $K[X]$ module.

Let $R$ be a ring, $M$ an $R$-module, and $A, B ≤ M$ two submodules of $M$ such that $M = A ⊕ B$. Prove that $M/A \cong B$.

Submodule of a semisimple module is just a subsum of decomposition

Is the (truncated) Witt ring an injective module over itself?

Is $\Bbb Z[i]$ flat as $\Bbb Z[2i]$-module?

Divisible module over an integral domain is not projective?

About free modules and finitely generated modules

Prove that $R[X_1,\dots,X_n] \otimes R[Y_1,\dots,Y_m] \cong R[X_1,\dots,X_n,Y_1,\dots Y_m] $

Unitary Ring of Endomorphisms.

Finite index submodules of finitely generated free modules.

length of minimal projective resolution and projective dimension

Is this true: $\operatorname{Hom}_R(S,R) \otimes_S P \cong \operatorname{Hom}_R(P,R)$?

Prove that a commutative right primitive ring is a field

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