Flashcards: Algebra

An operator is a mapping from one vector space or module to another.

Algebra (from Arabic "al-jabr" meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.

In Algebraic number theory, an algebraic integer is a complex number that is a root of some monic polynomial (a polynomial whose leading coefficient is 1) with coefficients in (the set of integers).

In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.

Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent n.

In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication.

In mathematics, a square is the result of multiplying a number by itself.

In mathematics, an operand is the object of a mathematical operation, a quantity on which an operation is performed.

In mathematics, a filtration is an indexed set Si of subobjects of a given algebraic structure S, with the index i running over some index set I that is a totally ordered set, subject to the condition that if i ≤ j in I, then Si ⊆ Sj.

In linear algebra, the determinant is a useful value that can be computed from the elements of a square matrix.

Elementary algebra encompasses some of the basic concepts of algebra, one of the main branches of mathematics.

In mathematics, an nth root of a number x, where n is usually assumed to be a positive integer, is a number r which, when raised to the power n yields x where n is the degree of the root.

In mathematics and computer algebra, factorization of polynomials or polynomial factorization is the process of expressing a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain.

In mathematics, the Gelfand–Naimark theorem states that an arbitrary C*-algebra A is isometrically *-isomorphic to a C*-algebra of bounded operators on a Hilbert space.

In algebra, the partial fraction decomposition or partial fraction expansion of a rational function (that is a fraction such that the numerator and the denominator are both polynomials) is the operation that consists in expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.

In mathematics, a closed-form expression is a mathematical expression that can be evaluated in a finite number of operations.

An algebraic solution or solution in radicals is a closed form expression, and more specifically a closed-form algebraic expression, that is the solution of an algebraic equation in terms of the coefficients, relying only on addition, subtraction, multiplication, division, raising to integer powers, and the extraction of nth roots (square roots, cube roots, and other integer roots).

In algebra, the content of a polynomial with integer coefficients (or, more generally, with coefficients in a unique factorization domain) is the greatest common divisor of its coefficients.

Goursat's lemma, named after the French mathematician Édouard Goursat, is an algebraic theorem about subgroups of the direct product of two groups.

The following outline is provided as an overview of and topical guide to algebra: Algebra is one of the main branches of mathematics.