Free moduleIn mathematics, a free module is a module that has a basis, that is, a generating set consisting of linearly independent elements. Every vector space is a free module, but, if the ring of the coefficients is not a division ring (not a field in the commutative case), then there exist non-free modules. Given any set S and ring R, there is a free R-module with basis S, which is called the free module on S or module of formal R-linear combinations of the elements of S. A free abelian group is precisely a free module over the ring Z of integers.
Abstraction (computer science)In software engineering and computer science, abstraction is: The process of removing or generalizing physical, spatial, or temporal details or attributes in the study of objects or systems to focus attention on details of greater importance; it is similar in nature to the process of generalization; the creation of abstract concept-objects by mirroring common features or attributes of various non-abstract objects or systems of study – the result of the process of abstraction.
International financial institutionsAn international financial institution (IFI) is a financial institution that has been established (or chartered) by more than one country, and hence is subject to international law. Its owners or shareholders are generally national governments, although other international institutions and other organizations occasionally figure as shareholders. The most prominent IFIs are creations of multiple nations, although some bilateral financial institutions (created by two countries) exist and are technically IFIs.
Generating set of a moduleIn mathematics, a generating set Γ of a module M over a ring R is a subset of M such that the smallest submodule of M containing Γ is M itself (the smallest submodule containing a subset is the intersection of all submodules containing the set). The set Γ is then said to generate M. For example, the ring R is generated by the identity element 1 as a left R-module over itself. If there is a finite generating set, then a module is said to be finitely generated. This applies to ideals, which are the submodules of the ring itself.
Abstraction (mathematics)Abstraction in mathematics is the process of extracting the underlying structures, patterns or properties of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena. Two of the most highly abstract areas of modern mathematics are and model theory.
European Committee for StandardizationThe European Committee for Standardization (CEN, Comité Européen de Normalisation) is a public standards organization whose mission is to foster the economy of the European Single Market and the wider European continent in global trading, the welfare of European citizens and the environment by providing an efficient infrastructure to interested parties for the development, maintenance and distribution of coherent sets of standards and specifications. The CEN was founded in 1961.
