SOME REMARKS ON WEAK AUTOMORPHISMS

Abstract

This chapter presents some remarks on weak automorphims. It discusses a general algebra and presents the condition when a bijection of the carrier of the algebra onto itself is said to be a weak automorphism. The chapter discusses some special general algebras called reducible algebras. The class of these algebras contains all linear spaces. An affine space is not reducible. This fact shows that the reduct of a reducible algebra need not be reducible. Any idempotent algebra that has a nontrivial weak automorphism is not reducible. The chapter also discusses weak automorphisms of reducible algebras.