All Questions

Wedderburn's Little Theorem states that every finite division ring is commutative. Perhaps even more surprising, this implies that every finite reduced ring is commutative. The proofs that I am aware ...

Is there any literature where the tools familiar from (multi)linear algebra are systematically transferred to the setting of semisimple modules over noncommutative rings? In fact this question is a ...

Let $R$ be a (commutative or non-commutative, associative) ring with unity, and let $a$ be an element of $R$ such that $r(a) = r(a^2)$, where $r(\cdot)$ denotes a right annihilator. It follows that $r(...

Let $R$ be a (commutative or non-commutative, associative) unital ring. Following Nicholson & Yousif [1, p. 21], we say that a right ideal $\mathfrak i$ of $R$ is extensive if every $R$-linear ...

Let $R$ be a (commutative or non-commutative) ring with identity. As usual, an idempotent $e \in R$ is primitive if $eR$ (the principal right ideal generated by $e$) is indecomposable as a right ...