Associations to the word «Algebraic»

ALGEBRAIC, adjective. Of, or relating to, algebra.

ALGEBRAIC, adjective. (mathematics) (of an expression, equation, or function) Containing only numbers, letters, and arithmetic operators.

ALGEBRAIC, adjective. (mathematics) (number theory) (said of a number) Which is a root of some polynomial whose coefficients are rational.

ALGEBRAIC, adjective. (chess) (of notation) Describing squares by file (referred to in intrinsic order rather than by the piece starting on that file) and rank, both with reference to a fixed point rather than a player-dependent perspective.

ALGEBRAIC CLOSURE, noun. (field theory) A field \(\bar{F}\) is an algebraic closure of a field \(F\) if it is algebraic over \(F\) and if every polynomial over F splits completely over \(\bar{F}\). (The first condition means that every element of \(\bar{F}\) is a root of some polynomial over \(F\), and the second condition means that any root of a polynomial over \(F\) must be found in \(\bar{F}\).)

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

ALGEBRAIC FUNCTION, noun. (algebra) Any function that only uses the operations of addition, subtraction, multiplication, division and raising to a rational power

ALGEBRAIC FUNCTIONS, noun. Plural of algebraic function

ALGEBRAIC GEOMETER, noun. A mathematician who specializes in algebraic geometry.

ALGEBRAIC GEOMETERS, noun. Plural of algebraic geometer

ALGEBRAIC GEOMETRY, noun. (mathematics) a branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry.

ALGEBRAIC INTEGER, noun. (mathematics) A number (real or complex) which is a root of a monic polynomial whose coefficients are integers.

ALGEBRAIC INTEGERS, noun. Plural of algebraic integer

ALGEBRAIC NOTATION, noun. A method for recording and describing the moves in a game of chess which employs a single uppercase letter for each piece and a letter-number coordinate for each square.

ALGEBRAIC NUMBER, noun. (mathematics) A complex number that is a root of a polynomial equation with rational coefficients.

ALGEBRAIC NUMBER FIELD, noun. (algebra) (field theory) number field

ALGEBRAIC NUMBER THEORY, noun. (mathematics) The subfield of number theory where algebraic numbers are studied using algebra.

ALGEBRAIC NUMBERS, noun. Plural of algebraic number

ALGEBRAIC STRUCTURE, noun. (algebra) One or more sets (carrier sets) together with a set of operations such that the sets are closed under the operations and are satisfying some axioms.

ALGEBRAIC TOPOLOGY, noun. That branch of topology that associates objects from abstract algebra to topological spaces.

ALGEBRAIC, adjective. Of or relating to algebra; "algebraic geometry".