Product may refer to:

Business

Product (business) In marketing, a product is an object, or system, or service made available for consumer use as of the consumer demand; it is anything that can be offered to a market to satisfy the desire or need of a customer. In retailing, products are of ...

, an item that serves as a solution to a specific consumer problem. *

Product (project management) {{more citations needed, date=January 2021 In project management under the PRINCE2 methodology, a product breakdown structure (PBS) is a tool for analysing, documenting and communicating the outcomes of a project, and forms part of the product ba ...

, a deliverable or set of deliverables that contribute to a business solution

Mathematics

Product (mathematics) In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called ''factors''. For example, 30 is the product of 6 and 5 (the result of multiplication), and x\c ...

Algebra

Direct product In mathematics, one can often define a direct product of objects already known, giving a new one. This generalizes the Cartesian product of the underlying sets, together with a suitably defined structure on the product set. More abstractly, one t ...

Set theory

Cartesian product In mathematics, specifically set theory, the Cartesian product of two sets ''A'' and ''B'', denoted ''A''×''B'', is the set of all ordered pairs where ''a'' is in ''A'' and ''b'' is in ''B''. In terms of set-builder notation, that is : A\ ...

of sets

Group theory

Direct product of groups In mathematics, specifically in group theory, the direct product is an operation that takes two groups and and constructs a new group, usually denoted . This operation is the group-theoretic analogue of the Cartesian product of sets and is o ...

Semidirect product In mathematics, specifically in group theory, the concept of a semidirect product is a generalization of a direct product. There are two closely related concepts of semidirect product: * an ''inner'' semidirect product is a particular way in w ...

Product of group subsets In mathematics, one can define a product of group subsets in a natural way. If ''S'' and ''T'' are subsets of a group ''G'', then their product is the subset of ''G'' defined by :ST = \. The subsets ''S'' and ''T'' need not be subgroups for this pro ...

Wreath product In group theory, the wreath product is a special combination of two groups based on the semidirect product. It is formed by the action of one group on many copies of another group, somewhat analogous to exponentiation. Wreath products are used ...

Free product In mathematics, specifically group theory, the free product is an operation that takes two groups ''G'' and ''H'' and constructs a new The result contains both ''G'' and ''H'' as subgroups, is generated by the elements of these subgroups, and ...

Zappa–Szép product In mathematics, especially group theory, the Zappa–Szép product (also known as the Zappa–Rédei–Szép product, general product, knit product, exact factorization or bicrossed product) describes a way in which a group can be constructed fr ...

(or knit product), a generalization of the direct and semidirect products

Ring theory

* Product of rings * Ideal operations, for product of

ideals Ideal may refer to: Philosophy * Ideal (ethics), values that one actively pursues as goals * Platonic ideal, a philosophical idea of trueness of form, associated with Plato Mathematics * Ideal (ring theory), special subsets of a ring considered ...

Linear algebra

Scalar multiplication In mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract algebra). In common geometrical contexts, scalar multiplication of a real Euclidean vector ...

Matrix multiplication In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the ...

* Inner product, on an

inner product space In mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an inner product. The inner product of two vectors in the space is a scalar, often ...

* Exterior product or wedge product *

Multiplication of vectors In mathematics, vector multiplication may refer to one of several operations between two (or more) vectors. It may concern any of the following articles: * Dot product – also known as the "scalar product", a binary operation that takes two vecto ...

: **

Dot product In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidean space. is an alg ...

Cross product In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E), and i ...

** Seven-dimensional cross product **

Triple product In geometry and algebra, the triple product is a product of three 3- dimensional vectors, usually Euclidean vectors. The name "triple product" is used for two different products, the scalar-valued scalar triple product and, less often, the vector ...

, in vector calculus *

Tensor product In mathematics, the tensor product V \otimes W of two vector spaces and (over the same Field (mathematics), field) is a vector space to which is associated a bilinear map V\times W \to V\otimes W that maps a pair (v,w),\ v\in V, w\in W to an e ...

Topology

Product topology In topology and related areas of mathematics, a product space is the Cartesian product of a family of topological spaces equipped with a natural topology called the product topology. This topology differs from another, perhaps more natural-seem ...

Algebraic topology

Cap product In algebraic topology the cap product is a method of adjoining a chain of degree ''p'' with a cochain of degree ''q'', such that ''q'' ≤ ''p'', to form a composite chain of degree ''p'' − ''q''. It was introduced by Eduard Čech in 1936, a ...

Cup product In mathematics, specifically in algebraic topology, the cup product is a method of adjoining two cocycles of degree ''p'' and ''q'' to form a composite cocycle of degree ''p'' + ''q''. This defines an associative (and distributive) graded commutat ...

Slant product In algebraic topology the cap product is a method of adjoining a chain of degree ''p'' with a cochain of degree ''q'', such that ''q'' ≤ ''p'', to form a composite chain of degree ''p'' − ''q''. It was introduced by Eduard Čech in 1936, a ...

Homotopy theory

Smash product In topology, a branch of mathematics, the smash product of two pointed spaces (i.e. topological spaces with distinguished basepoints) (''X,'' ''x''0) and (''Y'', ''y''0) is the quotient of the product space ''X'' × ''Y'' under the ...

Wedge sum In topology, the wedge sum is a "one-point union" of a family of topological spaces. Specifically, if ''X'' and ''Y'' are pointed spaces (i.e. topological spaces with distinguished basepoints x_0 and y_0) the wedge sum of ''X'' and ''Y'' is the qu ...

(or wedge product)

Category theory

* Internal product, in a

monoidal category In mathematics, a monoidal category (or tensor category) is a category \mathbf C equipped with a bifunctor :\otimes : \mathbf \times \mathbf \to \mathbf that is associative up to a natural isomorphism, and an object ''I'' that is both a left ...

Product (category theory) In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas of mathematics such as the Cartesian product of sets, the direct product of groups or ri ...

, a generalization of mathematical products *

Fibre product In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit of a diagram consisting of two morphisms and with a common codomain. The pullback is often w ...

or pullback ** Coproduct or pushout

Probability theory

* Wick product of random variables

Graph theory

Graph product In graph theory, a graph product is a binary operation on graphs. Specifically, it is an operation that takes two graphs and and produces a graph with the following properties: * The vertex set of is the Cartesian product , where and are ...

Music

* ''Product'' (Brand X album), 1979 * ''Product'' (De Press album), 1982 * ''Product'' (Sophie album), 2015 * ''Product'', a three-CD compilation set by

Buzzcocks Buzzcocks are an English punk rock band formed in Bolton, England in 1976 by singer-songwriter-guitarist Pete Shelley and singer-songwriter Howard Devoto. They are regarded as a seminal influence on the Manchester music scene, the independe ...

Other uses

Product (chemistry) Products are the species formed from chemical reactions. During a chemical reaction, reactants are transformed into products after passing through a high energy transition state. This process results in the consumption of the reactants. It can be ...

, the species formed from chemical reactions * Hairstyling product, such as hairspray or hair gel, generally referred to as simply "product"