Left ideals in matrix rings over finite fields

2017/11/25 by R. A. Ferraz, Ferraz, R. A., C. Polcino Milies +3
Mathematics · #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA

paper · pdf · doi:10.48550/arxiv.1711.09289

arxiv created 2017/11/25 · arxiv updated 2017/11/28

Abstract

It is well-known that each left ideals in a matrix rings over a finite field is generated by an idempotent matrix. In this work we compute the number of left ideals in these rings, the number of different idempotents generating each left ideal, and give explicitly a set of idempotent generators of all left ideals of a given rank.

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