Abstract
This chapter discusses a few algebraic structures. The term algebraic structure refers to a set with one or more finitary operations defined on it. Examples of algebraic structures include groups, rings, fields, and lattices. More complex structures can be defined by introducing multiple operations or different underlying sets, or by altering the defining axioms. Examples of more complex algebraic structures include vector spaces, modules, and algebras. The properties of specific algebraic structures are studied in abstract algebra. The general theory of algebraic structures has been formalized in universal algebra. Category theory is used to study the relationships between two or more classes of algebraic structures, often of different kinds. For example, Galois Theory studies the connection between certain fields and groups, algebraic structures of two different kinds.
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