In the history of mathematics, the generality of algebra was a phrase used by Augustin-Louis Cauchy to describe a method of argument that was used in the...

mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth...

In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations...

The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial...

Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins...

out in words. The idea of generality is implied in al-Khwarizmi's exposition, but he had no scheme for expressing algebraically the general propositions...

In abstract algebra, a Jordan algebra is a nonassociative algebra over a field whose multiplication satisfies the following axioms: x y = y x {\displaystyle...

In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

principle of the generality of algebra widely used in earlier work, particularly by Euler. Instead, Cauchy formulated calculus in terms of geometric ideas...

fundamental group of a topological space gives information about the topological space. In full generality, an algebraic structure may use any number of sets and...

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

laws of the structure can be directly applied to the new problem. In full generality, algebraic structures may involve an arbitrary collection of operations...

In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string...

Maclaurin Leonhard Euler Gauss Joseph Fourier Law of continuity History of calculus Generality of algebra Elementary Calculus: An Infinitesimal Approach...

acceptable by modern standards of mathematical rigour (in particular his reliance on the principle of the generality of algebra), his ideas led to many great...

Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure of a distinguished...

project of giving rigorous bases to infinitesimal calculus. In particular, he rejected the heuristic principle that he called the generality of algebra, which...

tool for studying algebraic gadgets; for example, a group can be described by a certain monad. Monads are used in the theory of pairs of adjoint functors...

stressed the importance of rigor in analysis. Rigor in this case meant the rejection of the principle of Generality of algebra (of earlier authors such as...

group of theorems based on the development of algebraic functions in series, relying in particular on the principle of the generality of algebra. A somewhat...

advantage of algebraic signal processing is its generality and portability. In the original formulation of algebraic signal processing by Puschel and Moura, the...

geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra is...

a scalar (the given coordinate of the vector). Because of the generality of the tensor algebra, many other algebras of interest can be constructed by...

linear algebra, which asserts: the number of columns of a matrix M is the sum of the rank of M and the nullity of M; and the dimension of the domain of a linear...

Appendix:Glossary of abstract algebra in Wiktionary, the free dictionary. Abstract algebra is the subject area of mathematics that studies algebraic structures...

is no general, explicit and exact algebraic formula for the roots of a polynomial with degree 5 or more. (Generality matters because any polynomial with...

does not reduce the generality, as this can be realized by subtracting the right-hand side from both sides. The most common type of equation is a polynomial...

generalized to the context of algebras and congruences. The isomorphism theorems were formulated in some generality for homomorphisms of modules by Emmy Noether...

assigned objects called K-groups. These are groups in the sense of abstract algebra. They contain detailed information about the original object but...

theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and...