Phrase Hound found 40 phrases and 9 compound words that contain algebras. The most common are listed below. Open algebras in the live search for definitions, filters, and the full list.
Phrases 40
- associative algebrasplural of associative algebra: An algebra over a ring (or more narrowly, an algebra over a field) whose bilinear product is associative.
- Boolean algebrasplural of Boolean algebra: An algebraic structure (Σ,∨,∧,∼,0,1) where ∨ and ∧ are idempotent binary operators, ∼ is a unary involutory operator (called "complement"), and 0 and 1 are nullary operators (i.e., constants), such that (Σ,∨,0) …
- Clifford algebrasplural of Clifford algebra: A unital associative algebra which generalizes the algebra of quaternions but which is not necessarily a division algebra; it is generated by a set of γᵢ (with i ranging from, say, 1 to n) such that the square …
- division algebrasplural of division algebra: A linear algebra such that its non-zero vectors form a multiplicative group.
- Jordan algebrasplural of Jordan algebra: A non-associative algebra over a field whose product satisfies the axioms (i) xy=yx (the commutative law) and (ii) (xy)(xx)=x(y(xx)) (the Jordan identity).
- Lie algebrasplural of Lie algebra: An algebra over a field whose bilinear product is alternating (or, equivalently for a bilinear product, anticommutative) and satisfies the Jacobi identity. Such a bilinear product is called a Lie bracket.
- Banach algebrasplural of Banach algebra: An associative algebra over the real or complex numbers (or over a non-Archimedean complete normed field) that is also a Banach space.
- Hopf algebrasplural of Hopf algebra: A structure that is simultaneously a unital associative algebra and a counital coassociative coalgebra, equipped with an antiautomorphism satisfying a certain property.
- variety of algebrasSynonym of variety (“an equational class in universal algebra”).
- quaternion algebrasplural of quaternion algebra: A particular kind of algebra, generalizing the classical quaternions: a four-dimensional central simple algebra over a field.
- Ockham algebrasplural of Ockham algebra: A bounded distributive lattice with a dual endomorphism (where “dual” means that it satisfies De Morgan’s laws).
- Hecke algebrasplural of Hecke algebra: A deformation of the group algebra of a Coxeter group.
- algebras over a fieldplural of algebra over a field: An algebra over a ring such that the ring is in fact a field. As a module over a field, such an algebra is in particular a vector space.
- Kac-Moody algebrasplural of Kac-Moody algebra: A Lie algebra, usually infinite-dimensional, that can be defined by generators and relations through a generalized Cartan matrix. They have applications in theoretical physics.
- Heyting algebrasplural of Heyting algebra: A bounded lattice, L, modified to serve as a model for a logical calculus by being equipped with a binary operation called "implies", denoted → (sometimes ⊃ or ⇒), defined such that (a→b)∧a ≤ b and, moreover …
- Azumaya algebrasplural of Azumaya algebra: A generalization of central simple algebras to R-algebras where R need not be a field.
- Albert algebrasplural of Albert algebra: A 27-dimensional exceptional Jordan algebra.
- alternative algebrasplural of alternative algebra: An algebra such that every subalgebra generated by two elements is associative.
- composition algebrasplural of composition algebra: A non-associative (not necessarily associative) algebra, A, over some field, together with a nondegenerate quadratic form, N, such that N(xy) = N(x)N(y) for all x, y ∈ A.
- matrix algebrasplural of matrix algebra: Generically, the arithmetic of matrices, involving matrix addition, scalar multiplication of matrices, matrix multiplication, and matrix inversion.
- polynomial algebrasplural of polynomial algebra: A polynomial ring.
- reduced algebrasplural of reduced algebra: An algebra over a reduced ring.
- shuffle algebrasplural of shuffle algebra: A Hopf algebra with a basis corresponding to words on some set, whose product is given by the shuffle product X ⧢ Y of two words X, Y: the sum of all ways of interlacing them. The interlacing is given by the …
- simple algebrasplural of simple algebra: An algebra that contains no nontrivial proper (two-sided) ideals and whose multiplication operation is not zero (i.e., there exist a and b such that ab ≠ 0).
- universal algebrasplural of universal algebra: A branch of mathematics dealing with equational classes of algebras, where similar theorems from disparate branches of algebra are unified.
Compound words 9
- subalgebrasplural of subalgebra: A closed subset of an algebra.
- superalgebrasplural of superalgebra: A type of algebra used in supersymmetry.
- polyalgebrasplural of polyalgebra
- pseudoalgebrasplural of pseudoalgebra: (mathematics)
- antialgebrasplural of antialgebra: The algebra of antisets, antigroups, antirings etc.
- hyperalgebrasplural of hyperalgebra: The formal group ring of a formal group law.
- multialgebrasplural of multialgebra: An algebra composed of a set and a family of multioperations on that set
- prealgebrasplural of prealgebra: A school (in the US, middle school) course that introduces students to concepts needed to learn algebra.
- semialgebrasplural of semialgebra: A class that is closed under intersection and semiclosed under set difference