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* Any ring, thought of as a category with only one object, is a preadditive category.

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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__

__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 thought

__Any__tragedy

**,**he maintains

**,**has six elements: plot

**,**character

**,**and

__thought__( the objects

**of**imitation )

**,**diction and melody ( the means

**of**imitation )

**,**and spectacle ( the manner

**of**imitation )

**.**

*****

__Any__

__thought__or idea expressed in

**a**language

**,**prepared in

**a**form suitable for transmission by any means

**of**communication

**.**

__Any__

**object**radiating sound

**,**including

**a**loudspeaker system

**,**can be

__thought__

**of**

**as**being composed

**of**combinations

**of**such simple point sources

**.**

Though having been gone for

**a**few episodes ( and__thought__to have been " retired "), Comic Book Guy made an appearance in an episode that aired later in the season**,**"__Any__Given Sundance ".__Any__government that uses neoliberal economic

__thought__for its right-wing policies can be effectively labelled neoliberal

**.**

__Any__suggestion

**of**these attributes and names being convinced

**of**

**as**separate

**is**

__thought__to entail polytheism

**.**

__Any__ordinal number can be made into

**a**topological space by endowing it

**with**the order topology ( since

**,**being well-ordered

**,**an ordinal

**is**in particular totally ordered ): in the absence

**of**indication to the contrary

**,**it

**is**always that order topology which

**is**meant when an ordinal

**is**

__thought__

**of**

**as**

**a**topological space

**.**

__Any__positive immunological effect

**is**

__thought__to be the result

**of**melatonin acting on high affinity receptors ( MT1 and MT2 ) expressed in immunocompetent cells

**.**

__Any__16-bit drivers and programs would patch or hook what they

__thought__was the real MS-DOS

**,**but which was in reality just

**a**decoy

**.**

His novel Babylon (" Generation П " or " Generation P "

**is**the Russian title ) bears on its cover the inscription**,**"__Any____thought__that occurs in the process**of**reading this book**is**subject to copyright**.**__Any__attempt to explain theoretical

__thought__without acknowledging non-theoretical factors

**is**destined to fall into irresolvable antinomies

**.**

__Any__solar religion or solar symbolism were not yet established in any useful form and it

**is**now

__thought__that king Raneb might actually have been the first king who adopted extended religious

__thought__about the sun and the sky

**.**

__Any__attempt to describe

**a**doctrine will reflect

**a**particular viewpoint

**,**and for that reason cannot be

__thought__

**of**

**as**definitive

**.**

Any and category

__Any__partially ordered set I can be considered

**as**

**a**small

__category__where the morphisms consist

**of**arrows i → j if and

**only**if i ≤ j

**.**

For 2009

**,**the winner in the " least likely to succeed "__category__was "__Any__name**of**the decade 2000 – 2009**,**such**as**: Naughties**,**Aughties**,**Oughties**,**Pot stickers**,**etc**.**
:-

__Any__concerted practice or__category__**of**concerted practices that improve the production or distribution**of**goods**,**or promotes technical or economic progress**,**while allowing consumers**a**fair share**of**the resulting benefit**,**and that does not:__Any__collection

**of**objects and morphisms defines

**a**( possibly large ) directed graph G

**.**If we let J be the free

__category__generated by G

**,**there

**is**

**a**universal diagram F: J → C whose image contains G

**.**The limit ( or colimit )

**of**this diagram

**is**the same

**as**the limit ( or colimit )

**of**the original collection

**of**objects and morphisms

**.**

__Any__preordered set ( P

**,**≤) forms

**a**small

__category__

**,**where the objects are the members

**of**P

**,**the morphisms are arrows pointing from x to y when x ≤ y

**.**

__Any__monoid ( any algebraic structure

**with**

**a**single associative binary operation and an identity element ) forms

**a**small

__category__

**with**

**a**single

**object**x

**.**

__Any__group can be seen

**as**

**a**

__category__

**with**

**a**single

**object**in which every morphism

**is**invertible ( for every morphism f there

**is**

**a**morphism g that

**is**both left and right inverse to f under composition ) by viewing the group

**as**acting on itself by left multiplication

**.**

__Any__directed graph generates

**a**small

__category__: the objects are the vertices

**of**the graph

**,**and the morphisms are the paths in the graph ( augmented

**with**loops

**as**needed ) where composition

**of**morphisms

**is**concatenation

**of**paths

**.**

*****quantification

__Any__morphism f: X → Y in

**a**

__category__

**with**pullbacks induces

**a**monotonous map acting by pullbacks ( A monotonous map

**is**

**a**functor if we consider the preorders

**as**categories ).

*****

__Any__partially ordered set can be interpreted

**as**

**a**

__category__: the objects are the elements

**of**

**,**and there

**is**

**a**single morphism from to if and

**only**if

**.**

*****

__Any__topological space can be viewed

**as**

**a**

__category__by taking the open sets

**as**objects

**,**and

**a**single morphism between two open sets and if and

**only**if

**.**

__Any__

__category__

**with**this property

**is**necessarily

**a**thin

__category__: for any two objects there can be at most

**one**morphism from

**one**

**object**to the other

**.**

#

__Any__group G may be regarded**as**an " abstract "__category__**with****one****object****,****,**and**one**morphism for each element**of**the group**.**__Any__directed poset can be considered

**as**

**a**small

__category__where the morphisms consist

**of**arrows if and

**only**if

**.**

__Any__Other Weapons ( AOWs )— this

**is**

**a**broad " catch-all "

__category__used to regulate any number

**of**firearms which the BATFE under the NFA enforces registration and taxation

**.**

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