Karl Jones: Created page with "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 opera..."

2016-09-11T19:45:58Z

Created page with "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 opera..."

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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 [[Axiom|axioms]].

== Description ==

Examples of algebraic structures include [[Group (mathematics)|groups]], [[Ring (mathematics)|rings]], [[Field (mathematics)|fields]], and [[Lattice (order)|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 space|vector spaces]], [[Module (mathematics)|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 ==

* [https://en.wikipedia.org/wiki/Algebraic_structure Algebraic structure] @ Wikipedia

[[Category:Mathematics]]

Algebraic structure - Revision history

Karl Jones: Created page with "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 opera..."