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* Any ring A is an algebra over its center Z ( A ), or over any subring of its center.

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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 is

__Any__claimant whose claim

__is__denied,

**or**

__is__approved for less than the full amount

**of**such claim, shall be entitled, under such regulations as the Commission may prescribe, to a hearing before the Commission,

**or**

**its**duly authorized representatives, with respect to such claim

**.**

__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__musician playing Beethoven here, where Beethoven was born,

__is__likely to examine his own interpretations with special care

**.**

__Any__action

__is__understood to create " seeds " in the mind that sprout into the appropriate results

**(**Pāli vipaka ) when they meet the right conditions

**.**

__Any__information may be conveyed by

**an**analog signal ; often such a signal

__is__a measured response to changes in physical phenomena, such as sound, light, temperature, position,

**or**pressure

**.**

__Any__quantity

**of**energy absorbed by the electron in excess

**of**this amount

__is__converted to kinetic energy according to the conservation

**of**energy

**.**

__Any__breach

**of**these laws

__is__a criminal offence and can lead to fine

**of**up to £ 5, 000

**or**six months in prison

**.**

The prohibition against retaliation

**or**coercion applies broadly to**any**individual**or**entity that seeks to prevent**an**individual from exercising his**or**her rights**or**to retaliate against him**or**her for having exercised those rights ...__Any__form**of**retaliation**or**coercion, including threats, intimidation,**or**interference,__is__prohibited if it__is__intended to interfere**.**__Any__work

**(**δW ) done must be done at the expense

**of**internal energy U, since no heat δQ

__is__being supplied from the surroundings

**.**

"

__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 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__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__).

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