New posts in modules

Examples proving why the tensor product does not distribute over direct products.

Reference request: compact objects in R-Mod are precisely the finitely-presented modules?

Prove that $\operatorname{Hom}_{\Bbb{Z}}(\Bbb{Q},\Bbb{Z}) = 0$ and show that $\Bbb{Q}$ is not a projective $\Bbb{Z}$-module.

Consequences of Proposition 1.1 on Semi-inner-product $A$-modules

Every $R$-module is free $\implies$ $R$ is a division ring

Number of subgroup $G<\Bbb Z^3$ such that $\Bbb Z^3/G\simeq \Bbb Z/3\Bbb Z\oplus\Bbb Z/3\Bbb Z$ [closed]

Applications of the Jordan-Hölder Theorem.

If $M$ is an $R$-module and $I\subseteq\mathrm{Ann}(M)$ an ideal, then $M$ has a structure of $R/I$-module

Showing that $\mathrm{Hom}_R(R/I, M) \cong \mathrm{Ann}_I(M)$

When $\operatorname{Hom}_{R}(M,N)$ is finitely generated as $\mathbb Z$-module or $R$-module?

Permutation module of $S_n$

Why does the ideal $(a+bi)$ have index $a^2+b^2$ in $\mathbb{Z}[i]$? [duplicate]

Finitely generated modules over a Noetherian ring are Noetherian

Why do direct limits preserve exactness?

Homomorphic image of a module

$R^n \cong R^m$ iff $n=m$

Intuitive explanation of Nakayama's Lemma

If $A$ an integral domain contains a field $K$ and $A$ over $K$ is a finite-dimensional vector space, then $A$ is a field. [duplicate]

Is $a^x \pmod{n} = (a\pmod{n})^{x \pmod{n}}$? [closed]

What exactly is the structure $IM$ for $I$ an ideal and $M$ a module?