Universal algebra

field of mathematics concerning the theory of algebraic structures

In logic, mathematics, and computer science, arity () is the number of arguments or operands taken by a function, operation or relation. In mathematics, arity may also be called rank, but this word can have many other meanings. In logic and philosophy, arity may also be called adicity and degree. In linguistics, it is usually named valency.

equivalence relation in algebra

notion in mathematical logic

set together with an interpretation of a given first-order language

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 the quotient set of the direct product of a family of structures. All factors need to have the same signature. The ultrapower is the special case of this construction in which all factors are equal.

In mathematics, a subalgebra is a subset of an algebra, closed under all its operations, and carrying the induced operations.

class of algebraic structures that is closed under subalgebras, homomorphic images and direct products

element of a generating set, a subset of an algebraic structure that allows specifying all elements of the structure

reflexive symmetric relation compatible with the operations of an algebraic structure

mathematical operator

concept in mathematics regarding sets operating on groups

subset of a structure that itself forms a structure

term in algebra

construction in universal algebra

Mathematical problem