Tarski's high school algebra problem
In mathematical logic, Tarski's high school algebra problem was a question posed by Alfred Tarski. It asks whether there are identities involving addition, multiplication, and exponentiation over the
Quasivariety
In mathematics, a quasivariety is a class of algebraic structures generalizing the notion of variety by allowing equational conditions on the axioms defining the class.
Subdirect product
In mathematics, especially in the areas of abstract algebra known as universal algebra, group theory, ring theory, and module theory, a subdirect product is a subalgebra of a direct product that depen
Locally finite variety
In universal algebra, a variety of algebras means the class of all algebraic structures of a given signature satisfying a given set of identities. One calls a variety locally finite if every finitely
Pseudoelementary class
In logic, a pseudoelementary class is a class of structures derived from an elementary class (one definable in first-order logic) by omitting some of its sorts and relations. It is the mathematical lo
Subalgebra
In mathematics, a subalgebra is a subset of an algebra, closed under all its operations, and carrying the induced operations. "Algebra", when referring to a structure, often means a vector space or mo
Algebra Universalis
Algebra Universalis is an international scientific journal focused on universal algebra and lattice theory. The journal, founded in 1971 by George Grätzer, is currently published by Springer-Verlag. H
Generator (mathematics)
In mathematics and physics, the term generator or generating set may refer to any of a number of related concepts. The underlying concept in each case is that of a smaller set of objects, together wit
Reduct
In universal algebra and in model theory, a reduct of an algebraic structure is obtained by omitting some of the operations and relations of that structure. The opposite of "reduct" is "expansion."
Congruence relation
In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure in
Post's lattice
In logic and universal algebra, Post's lattice denotes the lattice of all clones on a two-element set {0, 1}, ordered by inclusion. It is named for Emil Post, who published a complete description of t
Quasi-identity
In universal algebra, a quasi-identity is an implication of the form s1 = t1 ∧ … ∧ sn = tn → s = t where s1, ..., sn, t1, ..., tn, s, and t are terms built up from variables using the operation symbol
Stone algebra
In mathematics, a Stone algebra, or Stone lattice, is a pseudo-complemented distributive lattice such that a* ∨ a** = 1. They were introduced by and named after Marshall Harvey Stone. Boolean algebras
Clone (algebra)
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, …, xn) = xk,
* C is closed under (finitary multi
Quotient (universal algebra)
In mathematics, a quotient algebra is the result of partitioning the elements of an algebraic structure using a congruence relation.Quotient algebras are also called factor algebras. Here, the congrue
Universal algebra
Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures.For instance, rather than
Arity
Arity (/ˈærɪti/) is the number of arguments or operands taken by a function, operation or relation in logic, mathematics, and computer science. In mathematics, arity may also be named rank, but this w
Term algebra
In universal algebra and mathematical logic, a term algebra is a freely generated algebraic structure over a given signature. For example, in a signature consisting of a single binary operation, the t
BCK algebra
In mathematics, BCI and BCK algebras are algebraic structures in universal algebra, which were introduced by Y. Imai, K. Iséki and S. Tanaka in 1966, that describe fragments of the propositional calcu
Congruence-permutable algebra
In universal algebra, a congruence-permutable algebra is an algebra whose congruences commute under composition. This symmetry has several equivalent characterizations, which lend to the analysis of s
Graph algebra
In mathematics, especially in the fields of universal algebra and graph theory, a graph algebra is a way of giving a directed graph an algebraic structure. It was introduced by McNulty and Shallon, an
Basis (universal algebra)
In universal algebra, a basis is a structure inside of some (universal) algebras, which are called free algebras. It generates all algebra elements from its own elements by the algebra operations in a
Subdirectly irreducible algebra
In the branch of mathematics known as universal algebra (and in its applications), a subdirectly irreducible algebra is an algebra that cannot be factored as a subdirect product of "simpler" algebras.
Substructure (mathematics)
In mathematical logic, an (induced) substructure or (induced) subalgebra is a structure whose domain is a subset of that of a bigger structure, and whose functions and relations are restricted to the
Closure operator
In mathematics, a closure operator on a set S is a function from the power set of S to itself that satisfies the following conditions for all sets Closure operators are determined by their closed sets
Universal algebraic geometry
In algebraic geometry, universal algebraic geometry generalizes the geometry of rings to geometries of arbitrary varieties of algebras, so that every variety of algebras has its own algebraic geometry
Signature (logic)
In logic, especially mathematical logic, a signature lists and describes the non-logical symbols of a formal language. In universal algebra, a signature lists the operations that characterize an algeb
Jónsson term
In universal algebra, within mathematics, a majority term, sometimes called a Jónsson term, is a term t with exactly three free variables that satisfies the equations t(x, x, y) = t(x, y, x) = t(y, x,
Variety (universal algebra)
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 identities. For example, the groups form a varie
Structure (mathematical logic)
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 on it. Universal algebra studies structures that g
Group with operators
In abstract algebra, a branch of mathematics, the algebraic structure group with operators or Ω-group can be viewed as a group with a set Ω that operates on the elements of the group in a special way.
Ultraproduct
The ultraproduct is a mathematical construction that appears mainly in abstract algebra and mathematical logic, in particular in model theory and set theory. An ultraproduct is a quotient of the direc
Hidden algebra
Hidden algebra provides a formal semantics for use in the field of software engineering, especially for concurrent distributed object systems. It supports correctness proofs. Hidden algebra was studie
Tolerance relation
In universal algebra and lattice theory, a tolerance relation on an algebraic structure is a reflexive symmetric relation that is compatible with all operations of the structure. Thus a tolerance is l