Automorphisms of finite rings and applications to complexity of problems

Abstract

An important role played by automorphisms of algebraic structures in mathematics is discussed. Automorphisms capture the symmetries inherent in the structures and many important results have been proved by analyzing the automorphism group of the structure. Automorphisms also play a very important role in computer science specially in the finite rings because a number of algebraic problems reduce to questions about automorphisms and isomorphisms of finite rings. Automorphisms and isomorphisms of finite rings also have a number of useful applications in the complexity theory as well.