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* 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 ).

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## 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__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 R

__Any__subset

**of**

__R__

**<**

**sup**

**>**n

**</**

**sup**

**>**

**(**with its subspace topology

**)**that

**is**homeomorphic to another open subset

**of**

__R__

**<**

**sup**

**>**n

**</**

**sup**

**>**

**is**itself open.

Brown continued releasing recordings: in 1993

**,**he issued**the**album**,**Universal James**,**which included Brown's final Billboard charted single**,**" Can't Get__Any__Harder ", which peaked at # 76 on**the**US__R__& B chart**and**# 59 on**the**UK chart.__Any__formal series with has

**a**composition inverse provided

**is**an invertible element

**of**

__R__. The coefficients are found recursively from

**the**above formula for

**the**coefficients

**of**

**a**composition

**,**equating them with those

**of**

**the**composition identity X

**(**that

**is**1 at degree 1

**and**0 at every degree greater than 1

**)**.

*****

__Any__positive multiple

**of**

**the**repunit

__R__

**<**sub

**>**n

**</**sub ><

**sup**>( b )</

**sup**

**>**contains at least n nonzero digits in base b.

__Any__binary relation

__R__on

**a**set A

**can**generate

**a**natural partial order on

**the**R-cycle equivalence classes

**of**set A

**,**so that xRy implies ≥.

*****The Drug War in Mexico: By

__Any__Other Name it's Terrorism

**,**by Barnard

__R__. Thompson

**(**MexiData. info

**)**

__Any__totally ordered set that

**is**not isomorphic to

__R__but satisfies

**(**1

**)**–

**(**4

**)**

**is**known

**as**

**a**Suslin line.

__Any__physical object whose radius

__R__becomes less than or equal to

**the**Schwarzschild radius will undergo gravitational collapse

**and**become

**a**black hole.

__Any__proposed inverse

__R__

**of**F

**(**reconstruction formula

**,**in

**the**lingo

**)**would have to map to some subset

**of**.

*****

__Any__slave who evades capture for 20 days or more

**is**to

**be**publicly whipped for

**the**first offense

**;**branded with

**the**letter

__R__on

**the**

**right**cheek for

**the**second offense

**;**

**and**lose one ear if absent for thirty days for

**the**third offense

**;**

**and**castrated for

**the**fourth offense.

In early June

**,**Banks released**the**second single off**the**album**,**"__Any__Girl " featuring__R__& B singer Lloyd.
O. A.

__R__., who grew up in nearby Rockville**,**Maryland**,**recorded**the**live album__Any__Time Now at**the**9: 30 Club on November 23 – 24**,**2001.__Any__non-singular matrix S

**of**

**the**

**same**size

**is**said to transform A into another symmetric matrix B = SAS

**<**

**sup**

**>**T

**</**

**sup**

**>,**also

**of**order n

**,**

**where**S

**<**

**sup**

**>**T

**</**

**sup**

**>**

**is**

**the**transpose

**of**S. If A

**is**

**the**coefficient matrix

**of**some quadratic form

**of**

__R__

**<**

**sup**

**>**n

**</**

**sup**

**>,**then B

**is**

**the**matrix for

**the**

**same**form after

**the**change

**of**coordinates defined by S.

Lloyd C. Gardner

**,**" Pay__Any__Price: Lyndon Johnson**and****the**Wars for Vietnam ", Chicago: Ivan__R__. Dee**,**1995.

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.

0.241 seconds.