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Any ring can be seen as a preadditive category with a single object.
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Any and ring
* Any ring of matrices with coefficients in a commutative ring R forms an R-algebra under matrix addition and multiplication.
Any legal wrestler is open to attack from any direction at any time, including when they are downed, as long as they are within the ring area enclosed by the ring ropes.
Any number system that forms a commutative ring — for instance, the integers, the real numbers, and the complex numbers — can be extended to a wheel in which division by zero is always possible ; however, in such a case, " division " has a slightly different meaning.
* Any ring R can be considered as a one-object preadditive category ; the category of left modules over R is the same as the additive functor category Add ( R, Ab ) ( where Ab denotes the category of abelian groups ), and the category of right R-modules is Add ( R < sup > op </ sup >, Ab ).
Any prime number p gives rise to an ideal pO < sub > K </ sub > in the ring of integers O < sub > K </ sub > of a quadratic field K.
* Any algebra over a commutative ring K may be regarded as a purely even superalgebra over K ; that is, by taking A < sub > 1 </ sub > to be trivial.
Any n-dimensional formal group law gives an n dimensional Lie algebra over the ring R, defined in terms of the quadratic part F < sub > 2 </ sub > of the formal group law.
Any and can
Any alteration of one of these factors is distortion, although we generally use that word only for effects so pronounced that they can be stated quantitatively on the basis of standard tests.
Any reputable French interne can supply you with a dozen similar instances, and I'll presently recount a case out of my own personal experience, but, for the moment, let's resume our catalogue.
Any needy family living in San Francisco can obtain toys by writing to Christmas Toys, 676 Howard street, San Francisco 5, and listing the parent's name and address and the age and sex of each child in the family between the ages of 1 and 12.
Any breach of these laws is a criminal offence and can lead to fine of up to £ 5, 000 or six months in prison.
Any use of antibiotics can increase selective pressure in a population of bacteria to allow the resistant bacteria to thrive and the susceptible bacteria to die off.
Any given bookmaker will weight their odds so that no one customer can cover all outcomes at a profit against their books.
Any node in the data structure can be reached by starting at root node and repeatedly following references to either the left or right child.
Any Banach algebra ( whether it has an identity element or not ) can be embedded isometrically into a unital Banach algebra so as to form a closed ideal of.
* Any locally compact Hausdorff space can be turned into a compact space by adding a single point to it, by means of Alexandroff one-point compactification.
Any Sangiovese-based wine made according to the Chianti guidelines from these vineyards can be labelled and marked under the basic Chianti DOCG should the producer wish to use the designation.
Any units of angular measure can be used for declination, but it is customarily measured in the degrees ( ° ), minutes ( ' ), and seconds ( " ) of sexagesimal measure, with 90 ° equivalent to circle.
Any convex polyhedron can be distorted into a canonical form, in which a midsphere ( or intersphere ) exists tangent to every edge, such that the average position of these points is the center of the sphere, and this form is unique up to congruences.
Any person who uses the Spanish title of " Doctor " ( or " Dr .") without being included in this Government database can be prosecuted for fraud.
Any ellipse can be obtained by rotation and translation of a canonical ellipse with the proper semi-diameters.