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Any ring can be seen as a preadditive category with a single object.

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Wikipedia

## Some Related Sentences

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

**.**

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