Abstract
This is an introductory chapter. It provides first of all a short exposition of those facts of universal algebra that are needed in this book, then the definitions and theorems on polynomial algebras and the algebra of polynomial functions that are fundamental for all the chapters. Further these definitions and theorems are illustrated by special algebraic structures like rings, groups, lattices, and Boolean algebras. This chapter deals with systems of algebraic equations and related topics such as algebraic extensions and algebraic dependence for arbitrary algebras, and finally specializes to systems of equations over groups. It is based merely on investigates the composition of polynomials and polynomial functions for universal algebras in general, then for multi-operator groups in particular, and, again by specializing, for rings and groups.
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