Algebras

vector space equipped with a bilinear product

algebraic construction used in Euclidean geometry

algebra over a ring such that multiplication is associative

universal construction in multilinear algebra

In mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra; read as "star-algebra") is a mathematical structure consisting of two involutive rings and , where is commutative and has the structure of an associative algebra over . Involutive algebras generalize the idea of a number system equipped with conjugation, for example the complex numbers and complex conjugation, matrices over the complex numbers and conjugate transpose, and linear operators over a Hilbert space and Hermitian adjoints. However, it may happen that an algebra admits no involution.

graded module, where the grading has the structure of a monoid, in which ring multiplication respects the grading

algebra over a field with only invertible elements and zero

algebraic structure similar to ring but not necessarily having a multiplicative identity

theorem that the finite-dimensional associative division algebras over the reals are either the reals, the complex numbers, or the quaternions

algebra of all possible symmetric tensors over a vector space or ring module

differential algebra

finite-dimensional unital associative algebra with a compatible bilinear form

associative algebra together with a Lie bracket that also satisfies Leibniz's law

free object in the category of associative algebras

topological algebra associated to continuous groups

type of algebra over a field

deformation of the group algebra of a Coxeter group

In mathematics and theoretical physics, a superalgebra is a Z2-graded algebra. That is, it is an algebra over a commutative ring or field with a decomposition into "even" and "odd" pieces and a multiplication operator that respects the grading.

algebra over a ring that has a finite set of algebra generators

differential associative algebra with integer grading in which the differential has grading +1 (cohomological convention) or −1 (homological convention)

Associative Artinian algebra with a trivial Jacobson radical

linear representation of an associative algebra