Primary productionIn ecology, primary production is the synthesis of organic compounds from atmospheric or aqueous carbon dioxide. It principally occurs through the process of photosynthesis, which uses light as its source of energy, but it also occurs through chemosynthesis, which uses the oxidation or reduction of inorganic chemical compounds as its source of energy. Almost all life on Earth relies directly or indirectly on primary production. The organisms responsible for primary production are known as primary producers or autotrophs, and form the base of the food chain.
Category of ringsIn mathematics, the category of rings, denoted by Ring, is the whose objects are rings (with identity) and whose morphisms are ring homomorphisms (that preserve the identity). Like many categories in mathematics, the category of rings is , meaning that the class of all rings is proper. The category Ring is a meaning that the objects are sets with additional structure (addition and multiplication) and the morphisms are functions that preserve this structure.
Plant litterPlant litter (also leaf litter, tree litter, soil litter, litterfall or duff) is dead plant material (such as leaves, bark, needles, twigs, and cladodes) that have fallen to the ground. This detritus or dead organic material and its constituent nutrients are added to the top layer of soil, commonly known as the litter layer or O horizon ("O" for "organic"). Litter is an important factor in ecosystem dynamics, as it is indicative of ecological productivity and may be useful in predicting regional nutrient cycling and soil fertility.
Rings of JupiterThe planet Jupiter has a system of faint planetary rings. The Jovian rings were the third ring system to be discovered in the Solar System, after those of Saturn and Uranus. The main ring was discovered in 1979 by the Voyager 1 space probe and the system was more thoroughly investigated in the 1990s by the Galileo orbiter. The main ring has also been observed by the Hubble Space Telescope and from Earth for several years. Ground-based observation of the rings requires the largest available telescopes.
Product of ringsIn mathematics, a product of rings or direct product of rings is a ring that is formed by the Cartesian product of the underlying sets of several rings (possibly an infinity), equipped with componentwise operations. It is a direct product in the . Since direct products are defined up to an isomorphism, one says colloquially that a ring is the product of some rings if it is isomorphic to the direct product of these rings.
Rings of SaturnThe rings of Saturn are the most extensive ring system of any planet in the Solar System. They consist of countless small particles, ranging in size from micrometers to meters, that orbit around Saturn. The ring particles are made almost entirely of water ice, with a trace component of rocky material. There is still no consensus as to their mechanism of formation. Although theoretical models indicated that the rings were likely to have formed early in the Solar System's history, newer data from Cassini suggested they formed relatively late.
Flat moduleIn algebra, flat modules include free modules, projective modules, and, over a principal ideal domain, torsion free modules. Formally, a module M over a ring R is flat if taking the tensor product over R with M preserves exact sequences. A module is faithfully flat if taking the tensor product with a sequence produces an exact sequence if and only if the original sequence is exact. Flatness was introduced by in his paper Géometrie Algébrique et Géométrie Analytique.
Prime ministerA prime minister, premier or chief of cabinet is the head of the cabinet and the leader of the ministers in the executive branch of government, often in a parliamentary or semi-presidential system. Under those systems, a prime minister is not the head of state, but rather the head of government, serving as the principle administrator under either a monarch in a monarchy or under a president in a republican form of government.
Prime Minister of IndiaThe prime minister of India (IAST: ) is the head of government of the Republic of India. Executive authority is vested in the prime minister and his chosen Council of Ministers, despite the president of India being the nominal head of the executive. The prime minister is often the leader of the party or the coalition with a majority in the lower house of the Parliament of India, the Lok Sabha, which is the main legislative body in the Republic of India. The prime minister and their cabinet are at all times responsible to the Lok Sabha.
Prime Minister of the United KingdomThe prime minister of the United Kingdom is the head of government of the United Kingdom. The prime minister advises the sovereign on the exercise of much of the royal prerogative, chairs the Cabinet and selects its ministers. As modern prime ministers hold office by virtue of their ability to command the confidence of the House of Commons, they sit as members of Parliament. The office of prime minister is not established by any statute or constitutional document, but exists only by long-established convention, whereby the monarch appoints as prime minister the person most likely to command the confidence of the House of Commons.
Spirit (rover)Spirit, also known as MER-A (Mars Exploration Rover – A) or MER-2, is a Mars robotic rover, active from 2004 to 2010. Spirit was operational on Mars for sols or 3.3 Martian years ( days; ). It was one of two rovers of NASA's Mars Exploration Rover Mission managed by the Jet Propulsion Laboratory (JPL). Spirit landed successfully within the impact crater Gusev on Mars at 04:35 Ground UTC on January 4, 2004, three weeks before its twin, Opportunity (MER-B), which landed on the other side of the planet.
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.
