Automorphism group of the intersection graph of ideals over a matrix ring

Abstract

Let R be a ring with identity. The intersection graph of ideals of R, written as , is a graph which has all non-trivial left ideals of R as its vertices and two distinct non-trivial left ideals of R are adjacent if and only if . Let be a finite field with q elements, the ring of all matrices over . In this article, all automorphisms of are determined definitely.