Phrase Hound found 55 phrases and 23 compound words that contain algebra. The most common are listed below. Open algebra in the live search for definitions, filters, and the full list.
Phrases 55
- linear algebraThe branch of mathematics that deals with vectors, vector spaces, linear transformations and systems of linear equations.
- abstract algebraThe branch of mathematics concerned with algebraic structures, such as groups, rings, and fields.
- Boolean algebraAn 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) is a commutative monoid …
- universal algebraA branch of mathematics dealing with equational classes of algebras, where similar theorems from disparate branches of algebra are unified.
- Lie algebraAn 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.
- central simple algebraA finite-dimensional associative algebra over some field K that is a simple algebra and whose centre is exactly K.
- commutative algebraThe branch of algebra concerned with commutative rings and objects related to them (such as ideals and modules).
- Clifford algebraA 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 of each γᵢ is fixed to be …
- simple algebraAn 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).
- composition algebraA 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.
- vector algebraThe branch of mathematics that deals with vectors and operations on them.
- elementary algebraAn informally defined area of algebra considered suitable to be taught to secondary school students.
- homological algebraThe branch of mathematics dealing with homology and in particular with homological functors and the algebraic structures they entail.
- De Morgan algebraA bounded distributive lattice equipped with an involution (typically denoted ¬ or ~) which satisfies De Morgan's laws.
- Heyting algebraA 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, that x = a→b is the greatest …
- alternative algebraAn algebra such that every subalgebra generated by two elements is associative.
- k-algebraAn algebra over a field; a ring with identity together with an injective ring homomorphism from a field, k, to the ring such that the image of the field is a subset of the center of the ring and such that the image of the field’s unity is …
- Hurwitz algebraAny one of the unital composition algebras identified by Hurwitz's theorem (on composition algebras) as solutions to the Hurwitz problem.
- combinatorial commutative algebraA relatively new discipline in mathematics that combines techniques and concepts from combinatorics and commutative algebra, and in which the geometry of convex polytopes also plays a significant role.
- numerical linear algebraThe study of numerical analysis algorithms to solve mathematical problems in the field of linear algebra.
- Albert algebraA 27-dimensional exceptional Jordan algebra.
- division algebraA linear algebra such that its non-zero vectors form a multiplicative group.
- F-algebraA kind of generalization of the notion of algebraic structure.
- Jordan algebraA 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).
- matrix algebraGenerically, the arithmetic of matrices, involving matrix addition, scalar multiplication of matrices, matrix multiplication, and matrix inversion.
Compound words 23
- algebraicOf, or relating to, algebra.
- algebraicalPertaining to algebra or its laws.
- superalgebraA type of algebra used in supersymmetry.
- algebraismThe use of abstract logic and symbol manipulation as opposed to empirical observation.
- algebricianSynonym of algebraist: A mathematician who specializes in algebra.
- algebraizationconversion to algebraic form
- algebroidAn infinitesimal algebraic object associated with a groupoid
- dialgebraAlternative form of bialgebra: A particular form of vector space that is a compatible form of two algebras.
- algebraizeTo perform by algebra; to reduce to algebraic form.
- algebralikeResembling algebra.