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* 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.

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## Some Related Sentences

Any and algebra

__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__field

**may**

**be**used

**as**the scalars for

**a**vector space

**,**which

**is**the standard general context for linear

__algebra__

**.**

:“

__Any__linear map from V**to**an__algebra__**A**can**be**uniquely extended**to**an__algebra__homomorphism from T ( V )**to****A**.”**A**weight on

**a**Lie

__algebra__g

**over**

**a**field F

**is**

**a**linear map λ: g → F with λ ( y )= 0 for all x

**,**y in g

**.**

__Any__weight on

**a**Lie

__algebra__g vanishes on the derived

__algebra__and hence descends

**to**

**a**weight on the abelian Lie

__algebra__g /.

:

__Any__linear transformation f: V →**A**from V**to**an__algebra__**A****over****K**can**be**uniquely extended**to**an__algebra__homomorphism from T ( V )**to****A****as**indicated**by**the following**commutative**diagram:__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__affine group scheme

**is**the spectrum of

**a**

**commutative**Hopf

__algebra__(

**over**

**a**base S

**,**this

**is**given

**by**the relative spectrum of an O

**<**

**sub**

**>**S

**</**

**sub**>-

__algebra__).

Any and over

__Any__animal could when travelin' fast

**,**

**be**sent heels

__over__head

**by**the simple process of overtakin' the brute

**,**seizin' its tail

**,**and givin' the latter

**a**pull

**to**one side

**.**

"

__Any__threat of war Clovis could make would only**be**effective if they were neighbors**;**" it**is**nowhere written**that**Syagrius was handed__over__in 486 or 487**.**__Any__player

**may**declare the game

__over__at any time during his turn if either of two conditions

**is**true: one chain has 41 or more tiles

**,**or there

**is**at least one chain on the board and every chain on the board has 11 or more tiles

**.**

__Any__season ticket holder could put themselves forward for election

**,**with

**a**certain number of nominations

**,**and votes were cast

**by**all season ticket holders

__over__the age of 18

**.**

__Any__and all profits made from book deals or any movies about Lindh's experience will

**be**automatically handed

__over__

**to**the federal government

**.**

__Any__list of these would have

**to**include the Night of the Living Houses ( said

**to**

**be**the first comic strip

**to**enter the collection of the Louvre ) wherein Nemo and

**a**friend are chased down

**a**city street

**by**

**a**gang of tenement houses on legs

**;**the Walking Bed

**,**in which Nemo and Flip ride

__over__the rooftops on the increasingly long limbs of Nemo's bed ( see illustration ); and the Befuddle Hall sequence

**,**wherein Nemo and his friends attempt

**to**find their way out of

**a**funhouse environment of

**a**Beaux-Arts interior turned topsy-turvy

**.**

__Any__Hohenstaufen in Sicily was bound

**to**have claims

__over__the cities of Lombardy

**,**and

**as**

**a**check

**to**Manfred

**,**Urban IV introduced Charles of Anjou into the equation

**to**place the crown of the Two Sicilies in the hands of

**a**monarch amenable

**to**papal control

**.**

__Any__component of target velocity perpendicular

**to**the line of sight cannot

**be**determined

**by**using the Doppler effect alone

**,**but it can

**be**determined

**by**tracking the target's azimuth

__over__time

**.**

In July 2006

**,****a**book**,**' Peace at__Any__Price: How the World Failed Kosovo ', written**by**two former senior staffers at UNMIK**,**exposed**a**catalogue of errors and incompetence in the institution__over__its seven year history**.**__Any__large body of water upwind will impact lake-effect precipitation

**to**the lee of

**a**downwind lake

**by**adding moisture or pre-existing lake-effect bands

**,**which can re-intensify

__over__the downwind lake

**.**

__Any__production

__over__100 g must

**be**notified

**to**the OPCW and

**a**country can have

**a**stockpile of no more than one tonne of these chemicals

**.**

__Any__person

__over__the age of majority and of sound mind ( having appropriate mental capacity ) can draft his own will with or without the aid of

**a**lawyer

**.**

__Any__quadratic polynomial

__over__the complex numbers ( polynomials of the form where

**,**

**,**and ∈ ) can

**be**factored into an expression with the form using the quadratic formula

**.**

__Any__amount

__over__and above

**that**required

**to**maintain the capital at the beginning of the period

**is**profit

**.**

__Any__number of transputers could

**be**connected together

__over__

**even**longish links ( tens of metres )

**to**form

**a**single computing " farm ".

__Any__member of the priesthood who presides

__over__

**a**congregation can

**,**and often

**is**

**,**known

**as**" pastor " or ( if an elder ), " presiding elder ".

__Any__two adjacent conductors can

**be**considered

**a**capacitor

**,**although the capacitance will

**be**small unless the conductors are close together for long distances or

__over__

**a**large area

**.**

__Any__police entry of an individual's home always requires

**a**warrant ( for either search or arrest ), absent exigent circumstances

**,**or the free and voluntary consent of

**a**person with reasonably apparent use of or control

__over__the property

**.**

#

__Any__sequence satisfying the recurrence relation can**be**written uniquely**as****a**linear combination of solutions constructed in part**1****as**λ varies__over__all distinct roots of p ( t ).

Any and commutative

*****

__Any__

**ring**of matrices with coefficients in

**a**

__commutative__

**ring**R forms an R-algebra under matrix addition and multiplication

**.**

__Any__

__commutative__monoid

**is**endowed with its algebraic preordering ≤, defined

**by**x ≤ y if and only if there exists z such

**that**x + z = y

**.**

__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__

__commutative__semigroup

**is**

**a**medial magma

**,**and

**a**medial magma has an identity element if and only if it

**is**

**a**

__commutative__monoid

**.**

__Any__complete group variety ( variety here meaning reduced and geometrically irreducible separated scheme of finite type

**over**

**a**field )

**is**automatically

__commutative__

**,**

**by**an argument involving the action of conjugation on jet spaces of the identity

**.**

__Any__

__commutative__

**algebra**

**is**

**a**supercommutative

**algebra**if given the

**trivial**gradation ( i

**.**e

**.**all elements are

**even**).

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