(uncountable) A branch of mathematics dealing with equational classes of algebras, where similar theorems from disparate branches of algebra are unified.

(mathematics) The branch of mathematics concerned with algebraic structures, such as groups, rings, and fields.

(algebra, number theory) A real or complex number (more generally, an element of a number field) which is a root of a monic polynomial whose coefficients are integers; equivalently, an algebraic number whose minimal polynomial (lowest-degree polynomial of which it is a root and whose leading coefficient is 1) has integer coefficients.

(algebra) A mathematical equation in which one or both sides is an algebraic expression, such as 2x + 7y = 3.

(algebra, number theory) A complex number (more generally, an element of a number field) that is a root of a polynomial whose coefficients are integers; equivalently, a complex number (or element of a number field) that is a root of a monic polynomial whose coefficients are rational numbers.

(mathematics) The branch of mathematics that deals with vectors and operations on them.

(mathematics) The branch of mathematics that deals with vectors, vector spaces, linear transformations and systems of linear equations. / (algebra) an associative algebra

of, or relating to linear algebra

(mathematics) A branch of mathematics that studies algebraic varieties (solution sets of polynomial equations) and their generalisations, using techniques from both algebra (chiefly commutative algebra) and geometry.

(algebraic geometry) Informally, any function expressible using (only) the operations of addition, subtraction, multiplication, division and raising to a rational power; more precisely, any continuous function definable as the root of some polynomial equation.