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.
Read more about this topic: Outline Of Algebraic Structures
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