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

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...

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

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...

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

based on the number of operations they use and the laws they follow. Universal algebra constitutes a further level of generalization that is not limited...

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...

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

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

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...

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...

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

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

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

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...

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

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

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

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) →...

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

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...

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

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...

branch of mathematics known as universal algebra studies algebraic structures in general. From the universal algebra viewpoint, most structures can be...

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

expression Universal logic was coined by analogy with the expression Universal algebra by Jean-Yves Béziau. The aim was to develop Universal logic as a...

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