# Algebra/Related Articles

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A list of Citizendium articles, and planned articles, about Algebra.

## Bot-suggested topics

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• 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., x3+px2+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 ax2 + 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 i2 = −1, j2 = −1 and k2 = −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]