Algebraic Structure

Mathematical system consisting of a set and operations.

An algebraic structure is a mathematical system consisting of a set and one or more operations that satisfy certain axioms. It provides an abstract framework for studying mathematical objects.

/ˌældʒɪˈbræk ˈstrʌktʃər/

The term 'algebra' comes from the Arabic word ‘al-jabr’ meaning ‘restoration’ or ‘completion’, referring to the process of simplifying equations.

Algebraic structures are like toolboxes with a set of objects and rules for combining them, like numbers and addition in math.

What is an algebraic structure? It's a set with one or more operations defined on it
What are examples of algebraic structures? Groups, rings, and fields are common examples
Why are algebraic structures important? They provide a framework for studying mathematical systems

abstract algebra

mathematical system

group ring field module vector space

set operation

mathematical