Algebraic structure
In mathematics, and more specifically in abstract algebra, an algebraic structure is a set (called carrier set or underlying set) with one or more finitary operations defined on it that satisfies a list of axioms.
Description
Examples of algebraic structures include groups, rings, fields, and lattices.
More complex structures can be defined by introducing multiple operations, different underlying sets, or by altering the defining axioms.
Examples of more complex algebraic structures include vector spaces, modules, and algebra over a field.
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.
See also
- Abstract algebra
- Algebra over a field
- Axiom
- Category theory
- Field (mathematics)
- Free object
- Galois theory
- Group (mathematics)
- Lattice (order)
- List of algebraic structures
- Mathematical structure
- Module (mathematics)
- Ring (mathematics)
- Signature (logic)
- Structure (mathematical logic)
- Universal algebra
- Vector space
External links
- Algebraic structure @ Wikipedia
