Algebra
(1) Algebra is a subject taught in grade school and high school, sometimes referred to as "arithmetic", that includes the solution of polynomial equations in one or more variables and basic properties of functions and graphs. (2) In higher mathematics, the term algebra generally refers to abstract algebra, which involves advanced topics that deal with abstract algebraic structures rather than the usual number systems. (3) In topology, an algebra is a vector space that also possesses a vector multiplication.
Algebra is a college-level concept that would be first encountered in an abstract algebra course covering rings and fields.
Examples
| Boolean Algebra: |
A Boolean algebra is an algebra where the multiplication and addition also satisfy the properties of the AND and OR operations from logic. |
| Complex Number: |
A complex number is a number consisting of a real part and an imaginary part. A complex number is an element of the complex plane. |
| Gaussian Integer: |
A Gaussian integer is a complex number a + b i, where a and b are integers and i is the imaginary unit. |
| Lie Algebra: |
A Lie algebra is a nonassociative algebra corresponding to a Lie group. |
| Real Number: |
A real number is a number corresponding to a point on the real number line. |
Prerequisites
| Ring: |
In mathematics, a ring is an Abelian group together with a rule for multiplying its elements. |
| Vector Space: |
A vector space is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space. |
Classroom Articles on Rings and Fields
Classroom Articles on Abstract Algebra (Up to College Level)
