Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models")...

In universal algebra, a variety of algebras or equational class is the class of all algebraic structures of a given signature satisfying a given set of...

In mathematics, the universal enveloping algebra of a Lie algebra is the unital associative algebra whose representations correspond precisely to the...

In universal algebra, an abstract algebra A is called simple if and only if it has no nontrivial congruence relations, or equivalently, if every homomorphism...

homomorphic image theorem or as the first isomorphism theorem for universal algebra. Formally, let h : A → B {\displaystyle h:{\mathcal {A}}\to {\mathcal...

mathematics, a universal C*-algebra is a C*-algebra described in terms of generators and relations. In contrast to rings or algebras, where one can consider...

approach understands universal algebra as the study of one type of algebraic structures known as universal algebras. Universal algebras are defined in a general...

In universal algebra, a basis is a structure inside of some (universal) algebras, which are called free algebras. It generates all algebra elements from...

In mathematics, a universal geometric algebra is a type of geometric algebra generated by real vector spaces endowed with an indefinite quadratic form...

In algebraic geometry, universal algebraic geometry generalizes the geometry of rings to geometries of arbitrary varieties of algebras, so that every...

In universal algebra, an algebraic structure is called an algebra; this term may be ambiguous, since, in other contexts, an algebra is an algebraic structure...

groups is a single object in universal algebra, which is called the variety of groups. Before the nineteenth century, algebra was defined as the study of...

the exterior algebra, the symmetric algebra, Clifford algebras, the Weyl algebra and universal enveloping algebras. The tensor algebra also has two coalgebra...

additional bilinear operation. Algebras in universal algebra are far more general: they are a common generalisation of all algebraic structures. "Subalgebra"...

category theory, a universal property is a property that characterizes up to an isomorphism the result of some constructions. Thus, universal properties can...

symbols of a formal language. In universal algebra, a signature lists the operations that characterize an algebraic structure. In model theory, signatures...

algebra Symmetric algebra Tensor algebra Universal enveloping algebra Vertex operator algebra von Neumann algebra Weyl algebra Zinbiel algebra This is a list...

In the theory of C*-algebras, the universal representation of a C*-algebra is a faithful representation which is the direct sum of the GNS representations...

satisfies the following universal property: for every linear map f from V to a commutative algebra A, there is a unique algebra homomorphism g : S(V) →...

required in FIDE rated games. A form of long algebraic notation (without piece names) is also used by the Universal Chess Interface (UCI) standard, which is...

arise as Hopf algebras depending on an auxiliary parameter q or h, which become universal enveloping algebras of a certain Lie algebra, frequently semisimple...

overview, see Algebra. The bare word "algebra" may refer to: Elementary algebra Abstract algebra Algebra over a field In universal algebra, algebra has an axiomatic...

vector algebra Extension of scalars Monoidal category – Category admitting tensor products Tensor algebra – Universal construction in multilinear algebra Tensor...

representations of its Lie algebra. In the study of representations of a Lie algebra, a particular ring, called the universal enveloping algebra, associated with...

In universal algebra and mathematical logic, a term algebra is a freely generated algebraic structure over a given signature. For example, in a signature...

modules, Lie algebras, and other algebraic structures. In universal algebra, the isomorphism theorems can be generalized to the context of algebras and congruences...

rings, and fields. Pre-algebra Elementary algebra Boolean algebra Abstract algebra Linear algebra Universal algebra An algebraic equation is an equation...

graded algebra. The exterior algebra is universal in the sense that every equation that relates elements of V {\displaystyle V} in the exterior algebra is...

In universal algebra, a clone is a set C of finitary operations on a set A such that C contains all the projections πkn: An → A, defined by πkn(x1, …...

In algebraic geometry, a Cox ring is a sort of universal homogeneous coordinate ring for a projective variety, and is (roughly speaking) a direct sum...