# Algebra/Related Articles

From Citizendium, the Citizens' Compendium

< Algebra

*See also changes related to Algebra, or pages that link to Algebra or to this page or whose text contains "Algebra".*

## Parent topics

## Subtopics

- List of basic algebra topics
- List of mathematics articles
- Fundamental theorem of algebra
- Computer algebra system

## Bot-suggested topics

Auto-populated based on Special:WhatLinksHere/Algebra. Needs checking by a human.

- Absorbing element [r]: An element whose behaviour with respect to an algebraic binary operation is like that of zero with respect to multiplication.
^{[e]} - Absorption (mathematics) [r]: An identity linking a pair of binary operations.
^{[e]} - Abstract algebra [r]: Branch of mathematics that studies structures such as groups, rings, and fields.
^{[e]} - Algebraic geometry [r]: Discipline of mathematics that studies the geometric properties of the objects defined by algebraic equations.
^{[e]} - Algebraic independence [r]: The property of elements of an extension field which satisfy only the trivial polynomial relation.
^{[e]} - Algebraic number [r]: A complex number that is a root of a polynomial with rational coefficients.
^{[e]} - Associativity [r]: A property of an algebraic operation such as multiplication: a(bc) = (ab)c.
^{[e]} - Automorphism [r]: An isomorphism of an algebraic structure with itself: a permutation of the underlying set which respects all algebraic operations.
^{[e]} - Commutativity [r]: A property of a binary operation (such as addition or multiplication), that the two operands may be interchanged without affecting the result.
^{[e]} - Commutator [r]: A measure of how close two elements of a group are to commuting.
^{[e]} - Completing the square [r]: Rewriting a quadratic polynomial as a constant multiple of a linear polynomial plus a constant.
^{[e]} - Content (algebra) [r]: The highest common factor of the coefficients of a polynomial.
^{[e]} - Continuant (mathematics) [r]: An algebraic expression which has applications in generalized continued fractions and as the determinant of a tridiagonal matrix.
^{[e]} - Cubic equation [r]: A polynomial equation with of degree 3 (i.e.,
*x*^{3}+*px*^{2}+*qx*+r=0).^{[e]} - Cyclotomic polynomial [r]: A polynomial whose roots are primitive roots of unity.
^{[e]} - Derivation (mathematics) [r]: A map defined on a ring which behaves formally like differentiation: D(x.y)=D(x).y+x.D(y).
^{[e]} - Discriminant of a polynomial [r]: An invariant of a polynomial which vanishes if it has a repeated root: the product of the differences between the roots.
^{[e]} - Distributivity [r]: A relation between two binary operations on a set generalising that of multiplication to addition: a(b+c)=ab+ac.
^{[e]} - Division ring [r]: (or skew field), In algebra it is a ring in which every non-zero element is invertible.
^{[e]} - Euclid [r]: (ca. 325 BC - ca. 265 BC) Alexandrian mathematician and known as the father of geometry.
^{[e]} - Field (mathematics) [r]: An algebraic structure with operations generalising the familiar concepts of real number arithmetic.
^{[e]} - Field theory (mathematics) [r]: A subdiscipline of abstract algebra that studies fields, which are mathematical constructs that generalize on the familiar concepts of real number arithmetic.
^{[e]} - Frobenius map [r]: The p-th power map considered as acting on commutative algebras or fields of prime characteristic p.
^{[e]} - Fundamental Theorem of Algebra [r]: Any nonconstant polynomial whose coefficients are complex numbers has at least one complex number as a root.
^{[e]} - Galileo Galilei [r]: (1564-1642) Italian scientist, a pioneer in combining mathematical theory with systematic experiment in science, who came into conflict with the Church.
^{[e]} - Gaussian elimination [r]: Mathematical method for solving a set of linear equations.
^{[e]} - Geometry [r]: The mathematics of spacial concepts.
^{[e]} - Group theory [r]: Branch of mathematics concerned with groups and the description of their properties.
^{[e]} - Idempotent element [r]: An element or operator for which repeated application has no further effect.
^{[e]} - Identity element [r]: An element whose behaviour with respect to a binary operation generalises that of zero for addition or one for multiplication.
^{[e]} - Integral domain [r]: A commutative ring in which the product of two non-zero elements is again non-zero.
^{[e]} - International Mathematical Olympiad [r]: Annual mathematics contest for high school students from across the world.
^{[e]} - Kronecker delta [r]: A quantity depending on two subscripts which is equal to one when they are equal and zero when they are unequal.
^{[e]} - Krull dimension [r]: In a ring, one less than the length of a maximal ascending chain of prime ideals.
^{[e]} - Least common multiple [r]: The smallest integer which is divided evenly by all given numbers.
^{[e]} - Linear equation [r]: Algebraic equation, such as y = 2x + 7 or 3x + 2y − z = 4, in which the highest degree term in the variable or variables is of the first degree.
^{[e]} - Linear independence [r]: The property of a system of elements of a module or vector space, that no non-trivial linear combination is zero.
^{[e]} - Mathematics [r]: The study of quantities, structures, their relations, and changes thereof.
^{[e]} - Maxime Bôcher [r]: (1867–1918) American mathematician, specializing in the study of differential equations, series, and algebra.
^{[e]} - Measure theory [r]: Generalization of the concepts of length, area, and volume, to arbitrary sets of points not composed of line segments or rectangles.
^{[e]} - Modular arithmetic [r]: Form of arithmetic dealing with integers in which all numbers having the same remainder when divided by a whole number are considered equivalent.
^{[e]} - Monoid [r]: An algebraic structure with an associative binary operation and an identity element.
^{[e]} - Multiplication [r]: The binary mathematical operation of scaling one number or quantity by another (multiplying).
^{[e]} - Noetherian module [r]: Module in which every ascending sequence of submodules has only a finite number of distinct members.
^{[e]} - Noetherian ring [r]: A ring satisfying the ascending chain condition on ideals; equivalently a ring in which every ideal is finitely generated.
^{[e]} - Normal extension [r]: A field extension which contains all the roots of an irreducible polynomial if it contains one such root.
^{[e]} - Number theory [r]: The study of integers and relations between them.
^{[e]} - Number [r]: One of the fundamental concepts of mathematics, used for such purposes as counting, ordering, and measuring.
^{[e]} - Omar Khayyam [r]: Persian mathematician, astronomer and poet who died in 1131.
^{[e]} - Pascal's triangle [r]: A convenient tabular presentation for the binomial coefficients.
^{[e]} - Polynomial equation [r]: An equation in which a polynomial in one or more variables is set equal to zero.
^{[e]} - Polynomial ring [r]: Ring formed from the set of polynomials in one or more variables with coefficients in another ring.
^{[e]} - Polynomial [r]: A formal expression obtained from constant numbers and one or indeterminates; the function defined by such a formula.
^{[e]} - Quadratic equation [r]: An equation of the form
*ax*^{2}+*bx*+*c*= 0 where*a*,*b*and*c*are constants.^{[e]} - Quantity [r]: A mathematical concept that refers to a certain number of identical units of an observed group of units, e.g., a certain amount of apples in a fruit basket.
^{[e]} - Quaternions [r]: Numbers of form a + bi + cj + dk, where a, b, c and d are real, and i
^{2}= −1, j^{2}= −1 and k^{2}= −1.^{[e]} - Resultant (algebra) [r]: An invariant which determines whether or not two polynomials have a factor in common.
^{[e]} - Ring (mathematics) [r]: Algebraic structure with two operations, combining an abelian group with a monoid.
^{[e]} - Semigroup [r]: An algebraic structure with an associative binary operation.
^{[e]} - Separability (disambiguation) [r]:
*Add brief definition or description* - Set theory [r]: Mathematical theory that models collections of (mathematical) objects and studies their properties.
^{[e]} - Sine [r]: In a right triangle, the ratio of the length of the side opposite an acute angle (less than 90 degrees) and the length of the hypotenuse.
^{[e]} - Span (mathematics) [r]: The set of all finite linear combinations of a module over a ring or a vector space over a field.
^{[e]} - Splitting field [r]: A field extension generated by the roots of a polynomial.
^{[e]} - Vector (mathematics) [r]: A mathematical object with magnitude and direction.
^{[e]} - Weierstrass preparation theorem [r]: A description of a canonical form for formal power series over a complete local ring.
^{[e]}