For Ore's condition in graph theory, see Ore's theorem.
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In mathematics, especially in the area of algebra known as ring theory, the Ore condition is a condition introduced by Øystein Ore, in connection with the question of extending beyond commutative rings the construction of a field of fractions, or more generally localization of a ring. The right Ore condition for a multiplicative subset S of a ring R is that for a ∈ R and s ∈ S, the intersection aS ∩ sR ≠ ∅. A (non-commutative) domain for which the set of non-zero elements satisfies the right Ore condition is called a right Ore domain. The left case is defined similarly.[1]
^Cohn, P. M. (1991). "Chap. 9.1". Algebra. Vol. 3 (2nd ed.). p. 351.
in the area of algebra known as ring theory, the Orecondition is a condition introduced by Øystein Ore, in connection with the question of extending beyond...
scheme is defined in terms of Azumaya algebras. The Orecondition is a condition introduced by Øystein Ore, in connection with the question of extending beyond...
_{i}(\partial _{j})=0} for i > j {\displaystyle i>j} . Ore algebras satisfy the Orecondition, and thus can be embedded in a (skew) field of fractions...
{\displaystyle a} and b {\displaystyle b} in R {\displaystyle R} . Orecondition; condition related to constructing fractions in the noncommutative case. Total...
stand in an election Precipitation (chemistry) For ore deposits, see the "ore deposits" section in Ore. Deposit formation or fouling, the accumulation of...
by the PBW theorem. Similarly, a Weyl algebra is almost commutative. Orecondition Gelfand–Kirillov dimension Victor Ginzburg, Lectures on D-modules v...
condition for a ring with no zero divisors to be embeddable in a division ring (compare field of fractions in the commutative case). See also the Ore...
ring of quotients for non-commutative rings, where the absence of the Orecondition may impede the formation of the classical ring of quotients. This type...
lattices; There exists a Garside element. A Garside monoid satisfies the Orecondition for multiplicative sets and hence embeds in its group of fractions:...
Orion Electronics Ltd is a consumer electronics company headquartered in Budapest, Hungary.[citation needed] Orion supplies a wide range of brown and white...
lattice. Ore A left Ore domain is a (non-commutative) domain for which the set of non-zero elements satisfies the left Orecondition. A right Ore domain...
Iron Ore Company of Canada (often abbreviated to IOC) (French: Compagnie Minière IOC) is a Canadian-based producer of iron ore. The company was founded...
weathering causes the formation of many secondary and supergene ores: bauxite, iron ores, saprolitic gold, supergene copper, uranium, and heavy minerals...
manganese ore to manganese oxide (MnO), which is a leachable form. The ore then travels through a grinding circuit to reduce the particle size of the ore to...
Steelmaking is the process of producing steel from iron ore and/or scrap. In steelmaking, impurities such as nitrogen, silicon, phosphorus, sulfur and...
has allowed the economic recovery of valuable metals from much lower-grade ore than previously. Froth flotation is applied to a wide range of separations...
pelletizing iron ore. Pelletizing iron ore is undertaken due to the excellent physical and metallurgical properties of iron ore pellets. Iron ore pellets are...
submarine because she was carrying 10,800 long tons (10,973 t) of manganese ore used to produce munitions, but German authorities at the time, and subsequently...
generalizes earlier results by G. A. Dirac (1952) and Øystein Ore. Both Dirac's and Ore's theorems can also be derived from Pósa's theorem (1962). Hamiltonicity...
water, rocks, and soils. The metal is extracted from its principal mineral ores by the Kroll and Hunter processes. The most common compound, titanium dioxide...
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