Quotient ringIn ring theory, a branch of abstract algebra, a quotient ring, also known as factor ring, difference ring or residue class ring, is a construction quite similar to the quotient group in group theory and to the quotient space in linear algebra. It is a specific example of a quotient, as viewed from the general setting of universal algebra. Starting with a ring R and a two-sided ideal I in R, a new ring, the quotient ring R / I, is constructed, whose elements are the cosets of I in R subject to special + and ⋅ operations.
Open and closed mapsIn mathematics, more specifically in topology, an open map is a function between two topological spaces that maps open sets to open sets. That is, a function is open if for any open set in the is open in Likewise, a closed map is a function that maps closed sets to closed sets. A map may be open, closed, both, or neither; in particular, an open map need not be closed and vice versa. Open and closed maps are not necessarily continuous.
Open dataOpen data is data that is openly accessible, exploitable, editable and shared by anyone for any purpose. Open data is licensed under an open license. The goals of the open data movement are similar to those of other "open(-source)" movements such as open-source software, open-source hardware, open content, open specifications, open education, open educational resources, open government, open knowledge, open access, open science, and the open web. The growth of the open data movement is paralleled by a rise in intellectual property rights.
Quotient groupA quotient group or factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure (the rest of the structure is "factored" out). For example, the cyclic group of addition modulo n can be obtained from the group of integers under addition by identifying elements that differ by a multiple of and defining a group structure that operates on each such class (known as a congruence class) as a single entity.
Open textbookAn open textbook is a textbook licensed under an open license, and made available online to be freely used by students, teachers and members of the public. Many open textbooks are distributed in either print, e-book, or audio formats that may be downloaded or purchased at little or no cost. Part of the broader open educational resources movement, open textbooks increasingly are seen as a solution to challenges with traditionally published textbooks, such as access and affordability concerns.
Open accessOpen access (OA) is a set of principles and a range of practices through which research outputs are distributed online, free of access charges or other barriers. Under some models of open access publishing, barriers to copying or reuse are also reduced or removed by applying an open license for copyright. The main focus of the open access movement is "peer reviewed research literature". Historically, this has centered mainly on print-based academic journals.
Open standardAn open standard is a standard that is openly accessible and usable by anyone. It is also a common prerequisite that open standards use an open license that provides for extensibility. Typically, anybody can participate in their development due to their inherently open nature. There is no single definition, and interpretations vary with usage. The terms open and standard have a wide range of meanings associated with their usage.
