Division Ring


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division ring

[di′vizh·ən ‚riŋ]
(mathematics)
A ring in which the set of nonzero elements form a group under multiplication.
More generally, a nonassociative ring with nonzero elements in which, for any two elements a and b, there are elements x and y such that ax = b and ya = b.

Division Ring

 

a set of elements for which operations of addition, subtraction, multiplication, and division are defined that have the usual properties of the operations on numbers, except that the operation of multiplication need not be commutative. The set of quaternions is an example of a division ring. If multiplication of elements of a division ring is commutative, the division ring is a field.

References in periodicals archive ?
Using immunoelectron microscopy with antibodies to dynamin, gold particles indicating dynamin signals were not located directly on the filaments of the vesicle division ring in vivo, but only near the vesicle ring.
The 38-year-old eight division ring champ and current senator is due to face unknown Australian Jeff Horn in April for the first of a four-fight farewell tour arranged by his promoter Bob Arum.
Ms Tait told the court her division ring fences [euro]25million in its budget each year to provide various medical services and support to the 1,350 Hepatitis C sufferers in the country.
This will resolve the spatial organization of the fascinating patterns of Min proteins and chromatin that dictate the localization of the division ring.
Let [GAMMA] = (P, L) be a point-line geometry, let M be the set of point-line flags of [GAMMA], and let D be a division ring.
To contact the Huddersfield division ring 01484 425472 or 01484 533462.
By Martindale's theorem (18), R is then a primitive ring having nonzero socle H with C as the associated division ring.
Before the spindle has completely elongated to the tips of the cell, numerous microtubule nucleations can be observed at the center of the cell, where the division ring and septum eventually constrict to separate the two new cells [ILLUSTRATION FOR FIGURE 1B OMITTED].
Hua's fundamental theorem of geometry of matrices describes the general form of bijective maps on the space of all m X n matrices over a division ring D that preserve adjacency in both directions, explains Semrl.
Therefore H cannot contain two minimal orthogonal idempotent elements and so H = D, for a suitable division ring D finite dimensional over its center.
Largely in terms of graph theory but also describing some relations to linear codes, Pankov explores semilinear embeddings of vector spaces over division rings and the associated mappings of Grassmannians.
Siguiendo esta linea de investigacion, John Dauns publico algunos otros articulos de interes mas local como, por ejemplo, el articulo Integral domains which are not embeddable in division rings, publicado en Pacific J.

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