0
votes
1answer
165 views

Number of Minimal left ideals in the full matrix ring over a finite commutative local ring

Inspired with another QUESTION I would like to know the number of minimal left ideals of $M_n(R)$ in terms of $n$ and $R$ where $R$ is a finite local commutative ring with identity ?
0
votes
1answer
226 views

Chain of ideals in a complex algebra

Suppose $\mathfrak{A}$ is an unital algebra over complex numbers and $\mathfrak{J}$ is chain of left-ideals in $\mathfrak{A}$ ordered by inclusion such that none of its elements is countably ...
6
votes
2answers
2k views

Periodic matrices

A square matrix $M$ such that $M^{k+1}=M$, for some positive integer $k$, is called a periodic matrix. Can we characterize the periodic matrices in $\mathcal{M}_n(\mathbb{Z})$? If we replace ...