Abstract Algebra

What is an algebraic structure?

An algebraic structure is made up of a set (collection of objects called elements; for more information about sets, see “Foundations of Mathematics”) together with one or more operations on the set that satisfy certain axioms. The algebraic structures get their names depending on the operations and axioms. For example, algebraic structures include fields, groups, and rings—and many other structures with strange names such as loops, monoids, groupoids, semigroups, and quasigroups.


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