kidzsearch.com > wiki Explore:images videos games
Algebraic structure
KidzSearch Safe Wikipedia for Kids.
In mathematics an algebraic structure is a set with one, two or more binary operations on it.
The basic algebraic structures with one binary operation are the following:
 A set with a binary operation.
 A set with an operation which is associative
 A semigroup with an identity element
 A monoid where each element has a corresponding inverse element
 A group with a commutative operation
The basic algebraic structures with two binary operations are the following:
 A set with two operations, often called addition and multiplication. The set with the operation of addition forms a commutative group, and with the operation of multiplication it forms a semigroup (many people define a ring so that the set with multiplication is actually a monoid). Addition and multiplication in a ring satisfy the distributive property
 A ring whose multiplication is commutative
 A commutative ring where the set with multiplication is a group.
Examples are
 The whole numbers (natural numbers together with zero) with addition (or multiplication) is a monoid, but is not a group
 The integers with addition is a commutative group, but with multiplication is just a monoid
 The integers with addition and multiplication is a commutative ring, but not a field
 The rational numbers, the real numbers and the complex numbers with the ordinary addition and ordinary multiplication are fields.

