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...

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

Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as...

element of the system Variety (universal algebra), classes of algebraic structures defined by equations in universal algebra Variety (linguistics), a specific...

Clifford Bergman (2011). Universal Algebra: Fundamentals and Selected Topics. CRC Press. pp. 122–124, 137 (Maltsev varieties). ISBN 978-1-4398-5129-6...

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...

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...

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

as universal algebra studies algebraic structures in general. From the universal algebra viewpoint, most structures can be divided into varieties and...

Algebraic structure Universal algebra Variety (universal algebra) Congruence relation Free object Generating set (universal algebra) Clone (algebra)...

mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety. Thus the...

In algebraic geometry, a projective variety over an algebraically closed field k is a subset of some projective n-space P n {\displaystyle \mathbb {P}...

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

algebras are to set theory and ordinary propositional logic. Interior algebras form a variety of modal algebras. An interior algebra is an algebraic structure...

others. Abstract algebra Algebraic logic Abstract model theory Hierarchy (mathematics) Model theory Variety (universal algebra) Universal logic Font, 2003...

mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure...

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...

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

unipotent groups, as discussed below. For an algebraically closed field k, much of the structure of an algebraic variety X over k is encoded in its set X(k) of...

different aspects. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems...

Dual to ∃ is the unary operator ∀, the universal quantifier, defined as ∀x := (∃x′)′. A monadic Boolean algebra has a dual definition and notation that...

and a semisimple algebra over an algebraically closed field. The universal enveloping algebra of a Lie algebra is an associative algebra that can be used...

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 in model theory, a structure consists of a set along with a collection of finitary operations and relations that are defined...

quantum mechanics. It is a quotient of the universal enveloping algebra of the Heisenberg algebra, the Lie algebra of the Heisenberg group, by setting the...

A non-associative algebra (or distributive algebra) is an algebra over a field where the binary multiplication operation is not assumed to be associative...

quotient space in linear algebra. It is a specific example of a quotient, as viewed from the general setting of universal algebra. Starting with a ring R...

In mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket...

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 of...