Multiplicative maps on matrix algebras

TL;DR

This paper classifies all multiplicative maps on matrix algebras over a field of characteristic zero into three distinct categories using elementary methods.

Contribution

It provides a complete classification of multiplicative maps on matrix algebras, distinguishing trivial, degenerate, and non-degenerate cases.

Findings

Identifies three classes of multiplicative maps: trivial, degenerate, non-degenerate

Uses elementary methods for classification

Provides a comprehensive understanding of multiplicative maps on matrix algebras

Abstract

In this paper, we use elementary method to give a classification of the multiplicative maps on matrix algebra $M_{n}(\mF)$ over a field $\mF$ of characteristic $0$. All the multiplicative maps are classified into three classes: the trivial ones, the degenerate ones and the non-degenerate ones.