This chapter is more abstract than the other chapters in this book because it discusses algebraic systems in general and not just particular systems such as vector space or ring. The aim of this chapter on structure is to reveal some of the organization given to the algebraic concepts we have been implicitly using in the rest of the book. It formalizes the material of the other chapters and is the organizational spirit of this book. Despite the fact that it is here that the organization is laid bare we do not feel a study of this chapter is necessary for a productive use of this text. Analogously, one can become a very good mathematician without being a professional logician even though logical thought is central to mathematics.
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