Algebra

Major advances in the beginning of 20th century was the formalization of abstract algebra and topology; these two fields were deeply influenced by the pure mathematics philosophy.

Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems.

The converse of Lagrange's theorem states that if d is a divisor of the order of a group G, then there exists a subgroup H where |H| = d.

A vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied ("scaled") by numbers called scalars.

In mathematics, a ring is an algebraic structure consisting of a set with two binary operations typically called addition and multiplication

A complex number is an expression of the form a + bi, where a and b are real numbers, and i is an abstract symbol, the imaginary unit, whose meaning will be explained further below.

Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.

In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, which are central concepts in algebra and algebraic geometry.

Algebra studies two main families of equations: polynomial equations and, among them, the special case of linear equations.

it was named when algebra was synonymous with the theory of equations

a major unsolved problem in algebraic geometry and complex geometry

Gauss's proof relies firstly on the fact that constructibility is equivalent to expressibility of the trigonometric functions of the common angle in terms of arithmetic operations and square root extractions

Abstract algebra is the name that is commonly given to the study of algebraic structures.

Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures in general, not specific types of algebraic structures.

Budan's theorem is a theorem for bounding the number of real roots of a polynomial in an interval

a system of equations, also known as a set of simultaneous equations or an equation system, is a finite set of equations for which common solutions are sought

In mathematics, the Casas-Alvero conjecture is a problem about polynomials which have factors in common with their derivatives, proposed by Eduardo Casas-Alvero in 2001.

In mathematics, the Ax-Grothendieck theorem is a result about injectivity and surjectivity of polynomials that was proved independently by James Ax and Alexander Grothendieck.

In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to i

In elementary algebra, a difference of two squares is one squared number (the number multiplied by itself) subtracted from another

In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form ⁠ a x 2 + b x + c +b

In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup gene

In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.

z ) = x ⋅ y + x ⋅ z is always true in elementary algebra.

In algebra, the Bring radical or ultraradical of a real number a is the unique real root of the polynomial x 5 + x + a .

In mathematics and particularly in algebra, a system of equations (either linear or nonlinear) is called consistent if there is at

In mathematics, if A is an associative algebra over K, then an element a of A is an algebraic element over K, or just algebraic ov

In mathematics, more specifically in multilinear algebra, an alternating multilinear map is a multilinear map with all arguments b

In algebra, a sextic (or hexic) polynomial is a polynomial of degree six.

In abstract algebra, the sedenions form a 16-dimensional noncommutative and nonassociative algebra over the real numbers, usually

Sylvester's law of inertia is a theorem in matrix algebra about certain properties of the coefficient matrix of a real quadratic f

In abstract algebra, Ado's theorem is a theorem characterizing finite-dimensional Lie algebras.

Gamas's theorem is a result in multilinear algebra which states the necessary and sufficient conditions for a tensor symmetrized b

In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.

modern abstract algebra

abstract algebra

development of algebra

Fields are fundamental algebraic structures that are widely used in algebra, number theory, and many other areas of mathematics.

This work describes Bring's contribution to the algebraic solution of equations.

Brioschi published in Italy various algebraic theories

whose work on new algebra was an important step towards modern algebra

Nouvelle méthode pour la résolution des équations numériques

He was a friend of William Rowan Hamilton, and is credited both with inspiring Hamilton to discover the quaternions in October 1843 and then discovering their generalization the octonions himself (he called them octaves) later that same year.

A significant algebraist, he proved that a finite division algebra is a field (Wedderburn's little theorem), and part of the Artin-Wedderburn theorem on simple algebras.

Charles Hermite (French: [ʃaʁl ɛʁmit]; 24 December 1822-14 January 1901) was a French mathematician who studied analysis, number theory, and algebra.

Frank Morley (September 9, 1860, October 17, 1937) was a leading mathematician, known mostly for his teaching and research in the fields of algebra and geometry.

Bézout is also acknowledged for his work on algebra, despite being much occupied with his teaching duties, leaving him with relatively little time for algebra research.

Alexandru Froda (July 16, 1894, October 7, 1973) was a Romanian mathematician with contributions in the field of mathematical analysis, algebra, number theory and rational mechanics.

Arthur Cayley (; 16 August 1821-26 January 1895) was an English mathematician who worked mostly on algebra.

Sir William Rowan Hamilton (4 August 1805-2 September 1865) was an Irish mathematician, physicist, and astronomer who made numerous major contributions to algebra, classical mechanics, and optics.

Algebra Polynomials

Algebra Scalar Algebra

Algebra Algebraic Equations

Algebra Vector Algebra

Algebra Algebraic Equations

Algebra General Algebra

Algebra Vector Algebra

Algebra Sums

Algebra Forms

Algebra Algebraic Equations

Algebra Algebraic Equations

Algebra Quaternions and Clifford Algebras

In mathematics, the octonions are a normed division algebra over the real numbers, a kind of hypercomplex

of P. It follows from this (and the fundamental theorem of algebra) that, if the degree of a real polynomial is

In mathematics, the quaternions form a number system similar to the complex numbers, with the usual arithmetical operations of addition

Eisenstein's criterion gives a sufficient condition for a polynomial with integer coefficients to be irreducible over the rational numbers -

by René Descartes in his La Géométrie, counts the roots of a polynomial by examining sign changes in its coefficients.

Joseph Hidulphe Vincent-is a theorem that isolates the real roots of polynomials with rational coefficients. Even though Vincent's

after the Italian mathematician Giacomo Candido, is an identity for real numbers. It states that for two arbitrary real numbers

polynomial to be irreducible

In mathematics, the multinomial theorem describes how to expand a power of a sum in terms of powers of the terms in that sum.

In mathematics, a quintic function is a function of the form g ( x ) = a x 5 + b

In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's

In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B

a thesis on alternative algebras

who worked in abstract algebra, functional analysis and topological vector spaces

Hyman Bass is an American mathematician, known for work in algebra and in mathematics education.

Algebra Polynomials

Alexander Ostrowski was a Ukrainian-born mathematician who worked on a wide variety of topics in both analysis and algebra.

Christoff Rudolff was a German mathematician whose book Coss is the first German algebra book.

Ernst Witt was a German mathematician and a leading algebraist. He proved important results on Lie algebras.

Heinrich Weber was a German mathematician whose main work was in algebra, number theory, analysis and applications of analysis to mathematical physics.

Garrett Birkhoff was an American mathematician best known for the algebra book he wrote with Saunders Mac Lane.

Girolamo Cardan or Cardano was an Italian doctor and mathematician who is famed for his work Ars Magna which was the first Latin treatise devoted solely to algebra. In it he gave the methods of solution of the cubic and quartic equations which he had learnt from Tartaglia.

Ferrari was an Italian scholar who started as Cardan's secretary and went on to devise the solution of the quartic equation.

Tartaglia was an Italian mathematician who was famed for his algebraic solution of cubic equations which was eventually published in Cardan's Ars Magna .

Rafael Bombelli was an Italian mathematician who wrote an influential algebra text and made free use of both negative numbers and complex numbers.