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...

Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems...

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...

a quotient algebra is the result of partitioning the elements of an algebraic structure using a congruence relation. Quotient algebras are also called...

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

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

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

algebras has its own algebraic geometry. The two terms algebraic variety and variety of algebras should not be confused. Algebraic geometry Universal...

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...

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 mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

become short and elegant if the universal property is used rather than the concrete details. For example, the tensor algebra of a vector space is slightly...

{\displaystyle F} , with specific properties as defined below. For both algebras and coalgebras,[clarification needed] a functor is a convenient and general...

objects (also called quotient algebras in universal algebra, and cokernels in category theory). For many types of algebraic structure, the fundamental theorem...

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

the college until 1910, spending the 1890s writing his Treatise on Universal Algebra (1898), and the 1900s collaborating with his former pupil, Bertrand...

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

a lower bound. Thus, the partial order defined by the meet in the universal algebra approach coincides with the original partial order. Conversely, if...

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 abstract algebra, a magma, binar, or, rarely, groupoid is a basic kind of algebraic structure. Specifically, a magma consists of a set equipped with...

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) →...

formalisms of universal algebra are an important tool for many order theoretic considerations. Beside formalizing orders in terms of algebraic structures...

ring). *-algebra Affine Lie algebra Akivis algebra Algebra for a monad Albert algebra Alternative algebra AW*-algebra Azumaya algebra Banach algebra Birman–Wenzl...

branch of mathematics known as universal algebra (and in its applications), a subdirectly irreducible algebra is an algebra that cannot be factored as a...

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

and algebraic description of models appropriate for the study of various logics (in the form of classes of algebras that constitute the algebraic semantics...