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The following outline is provided as an overview of and topical guide to algebraic structures: In mathematics, there are many types of algebraic structures which are studied. Abstract algebra is primarily the study of specific algebraic structures and their properties. Algebraic structures may be viewed in different ways, however the common starting point of algebra texts is that an algebraic object incorporates one or more sets with one or more binary operations or unary operations satisfying a collection of axioms. Another branch of mathematics known as universal algebra studies algebraic structures in general. From the universal algebra viewpoint, most structures can be divided into varieties and quasivarieties depending on the axioms used. Some axiomatic formal systems that are neither varieties nor quasivarieties, called ''nonvarieties'', are sometimes included among the algebraic structures by tradition. Concrete examples of each structure will be found in the articles listed. Algebraic structures are so numerous today that this article will inevitably be incomplete. In addition to this, there are sometimes multiple names for the same structure, and sometimes one name will be defined by disagreeing axioms by different authors. Most structures appearing on this page will be common ones which most authors agree on. Other web lists of algebraic structures, organized more or less alphabetically, include (Jipsen ) and (PlanetMath. ) These lists mention many structures not included below, and may present more information about some structures than is presented here. == Study of algebraic structures == Algebraic structures appear in most branches of mathematics, and students can encounter them in many different ways. *Beginning study: In American universities, groups, vector spaces and fields are generally the first structures encountered in subjects such as linear algebra. They are usually introduced as sets with certain axioms. *Advanced study: * *Abstract algebra studies properties of specific algebraic structures. * *Universal algebra studies algebraic structures abstractly, rather than specific types of structures. * * *Varieties * *Category theory studies interrelationships between different structures, algebraic and non-algebraic. To study a non-algebraic object, it is often useful to use category theory to relate the object to an algebraic structure. * * *Example: The fundamental group of a topological space gives information about the topological space. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Outline of algebraic structures」の詳細全文を読む スポンサード リンク
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