New posts in abstract-algebra

Interesting Property of $(\Bbb Z_n,+)$

The torsion submodule of $\prod \mathbb{Z}_p$ is not a direct summand of $\prod \mathbb{Z}_p$

Why is cofiniteness included in the definition of direct sum of submodules?

Problem in the "proof" of Eisenstein's criterion on irreducibility.

Can we conclude that this group is cyclic? [duplicate]

Frattini subgroup is set of nongenerators

Why are there $12$ automorphisms of $\Bbb Z\oplus \Bbb Z_{3}$?

$L$ is an extension of $K$, if $L$ is a $K$-algebra

Prove that $I \subseteq R$ is prime if and only if $R/I$ is an integral domain.

Prove that the tensor product of non algebraic extensions is not a field

A module is projective iff it has a projective basis

Understanding Serre-Chevalley relations

$\exists x \in R$ and $\exists n \in\mathbb{N}$ such that $x^{n+1} = x^n \implies x^2 = x$

This polynomial has integer coefficient

Characterization of nonabelian group $G$ such that for all $x,y\in G$, $xy\neq yx\implies x^2=y^2$.

Normal extension of rational complex fields

Suppose R is a commutative ring, M is the maximum ideal of R, and R/M is not a field. Prove: (R/M)² = 0.

The root system of $sl(3,\mathbb C)$

Characterize finite dimensional algebras without nilpotent elements

A sufficient condition for a domain to be Dedekind?