Algebraic may refer to any subject related to

algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

in mathematics and related branches like

algebraic number theory Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic ob ...

and

algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...

. The word algebra itself has several meanings. Algebraic may also refer to: *

Algebraic data type In computer programming, especially functional programming and type theory, an algebraic data type (ADT) is a kind of composite data type, i.e., a data type formed by combining other types. Two common classes of algebraic types are product ty ...

, a datatype in computer programming each of whose values is data from other datatypes wrapped in one of the constructors of the datatype *

Algebraic number In mathematics, an algebraic number is a number that is a root of a function, root of a non-zero polynomial in one variable with integer (or, equivalently, Rational number, rational) coefficients. For example, the golden ratio (1 + \sqrt)/2 is ...

s, a complex number that is a root of a non-zero polynomial in one variable with integer coefficients *

Algebraic function In mathematics, an algebraic function is a function that can be defined as the root of an irreducible polynomial equation. Algebraic functions are often algebraic expressions using a finite number of terms, involving only the algebraic operati ...

s, functions satisfying certain polynomials *

Algebraic element In mathematics, if is an associative algebra over , then an element of is an algebraic element over , or just algebraic over , if there exists some non-zero polynomial g(x) \in K /math> with coefficients in such that . Elements of that are no ...

, an element of a field extension which is a root of some polynomial over the base field *

Algebraic extension In mathematics, an algebraic extension is a field extension such that every element of the larger field is algebraic over the smaller field ; that is, every element of is a root of a non-zero polynomial with coefficients in . A field extens ...

, a field extension such that every element is an algebraic element over the base field * Algebraic definition, a definition in mathematical logic which is given using only equalities between terms *

Algebraic structure In mathematics, an algebraic structure or algebraic system consists of a nonempty set ''A'' (called the underlying set, carrier set or domain), a collection of operations on ''A'' (typically binary operations such as addition and multiplicatio ...

, a set with one or more finitary operations defined on it * Algebraic, the order of entering operations when using a calculator (contrast

reverse Polish notation Reverse Polish notation (RPN), also known as reverse Łukasiewicz notation, Polish postfix notation or simply postfix notation, is a mathematical notation in which operators ''follow'' their operands, in contrast to prefix or Polish notation ...

) * Algebraic sum, a summation of quantities that takes into account their signs; e.g. the algebraic sum of 4, 3, and -8 is -1.

See also