Central simple algebraIn ring theory and related areas of mathematics a central simple algebra (CSA) over a field K is a finite-dimensional associative K-algebra A which is simple, and for which the center is exactly K. (Note that not every simple algebra is a central simple algebra over its center: for instance, if K is a field of characteristic 0, then the Weyl algebra is a simple algebra with center K, but is not a central simple algebra over K as it has infinite dimension as a K-module.
Data integrationData integration involves combining data residing in different sources and providing users with a unified view of them. This process becomes significant in a variety of situations, which include both commercial (such as when two similar companies need to merge their databases) and scientific (combining research results from different bioinformatics repositories, for example) domains. Data integration appears with increasing frequency as the volume (that is, big data) and the need to share existing data explodes.
Weyl's theorem on complete reducibilityIn algebra, Weyl's theorem on complete reducibility is a fundamental result in the theory of Lie algebra representations (specifically in the representation theory of semisimple Lie algebras). Let be a semisimple Lie algebra over a field of characteristic zero. The theorem states that every finite-dimensional module over is semisimple as a module (i.e., a direct sum of simple modules.) Weyl's theorem implies (in fact is equivalent to) that the enveloping algebra of a finite-dimensional representation is a semisimple ring in the following way.
Divisible groupIn mathematics, especially in the field of group theory, a divisible group is an abelian group in which every element can, in some sense, be divided by positive integers, or more accurately, every element is an nth multiple for each positive integer n. Divisible groups are important in understanding the structure of abelian groups, especially because they are the injective abelian groups. An abelian group is divisible if, for every positive integer and every , there exists such that .
Data curationData curation is the organization and integration of data collected from various sources. It involves annotation, publication and presentation of the data such that the value of the data is maintained over time, and the data remains available for reuse and preservation. Data curation includes "all the processes needed for principled and controlled data creation, maintenance, and management, together with the capacity to add value to data".
School libraryA school library (or a school library media center) is a library within a school where students, staff, and often, parents of a public or private school have access to a variety of resources. The goal of the school library media center is to ensure that all members of the school community have equitable access "to books and reading, to information, and to information technology." A school library media center "uses all types of media... is automated, and utilizes the Internet [as well as books] for information gathering.
Semi-simplicityIn mathematics, semi-simplicity is a widespread concept in disciplines such as linear algebra, abstract algebra, representation theory, , and algebraic geometry. A semi-simple object is one that can be decomposed into a sum of simple objects, and simple objects are those that do not contain non-trivial proper sub-objects. The precise definitions of these words depends on the context. For example, if G is a finite group, then a nontrivial finite-dimensional representation V over a field is said to be simple if the only subrepresentations it contains are either {0} or V (these are also called irreducible representations).
PipelineA pipeline is a system of pipes for long-distance transportation of a liquid or gas, typically to a market area for consumption. The latest data from 2014 gives a total of slightly less than of pipeline in 120 countries around the world. The United States had 65%, Russia had 8%, and Canada had 3%, thus 76% of all pipeline were in these three countries. Pipeline and Gas Journal'''s worldwide survey figures indicate that of pipelines are planned and under construction.
