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* Any ring of characteristic n is a ( Z / nZ )- algebra in the same way.

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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 characteristic

__Any__mutations for

**the**preference opposite to

**the**given

__characteristic__, though tending to promote survival against ecological selection, nevertheless tend not to survive

**in**

**the**gene pool because male offspring that result from matings based on

**the**preference are less sexually attractive to

**the**majority

**of**

**the**females

**in**

**the**population, and thus infrequently chosen as mates

**.**

Limiting:

__Any__process by which**a**specified__characteristic__**(**usually amplitude )**of****the**output**of****a**device**is**prevented from exceeding**a**predetermined value**.**
Note that for orientable compact surfaces without boundary,

**the**Euler__characteristic__equals, where**is****the**genus**of****the**surface:__Any__orientable compact surface without boundary**is**topologically equivalent to**a**sphere with some handles attached, and counts**the**number**of**handles**.**__Any__electromagnetic radiation consists

**of**an electric field component E and

**a**magnetic field component H

**.**In

**the**far-field,

**the**relationship between

**the**electric field component E and

**the**magnetic component H

**is**that

__characteristic__

**of**any freely propagating wave, where

**(**

**in**units where c = 1 ) E

**is**equal to H at any point

**in**space

**.**

*"

__Any__form**of**cultural knowledge or social activity__characteristic__**of****a**social group and**/**or cultural group that can be recognized by other groups such as Western anthropologists, but not necessarily by**the**group**of**origin, as mathematical knowledge or mathematical activity ".__Any__definite conclusion to Cynewulf being either Northumbrian or Mercian has been hard to come by, but linguistic evidence suggests that

**the**medial e

**in**

**the**signed Cynewulf would have, during

**the**broad window period

**of**Cynewulf ’ s existence, been

__characteristic__

**of**

**a**Mercian dialect

**.**

__Any__language,

**in**Bakhtin's view, stratifies into many voices: " social dialects,

__characteristic__group behavior, professional jargons, generic languages, languages

**of**generations and age groups, tendentious languages, languages

**of**

**the**authorities,

**of**various circles and

**of**passing fashions

**.**

:; Cavity back:

__Any__iron whose design__characteristic__**is**such that**the**weight**is**distributed primarily around**the**outer edges**of****the**club-head**in**order to maximize forgiveness on off-center hits**.**__Any__semiconductor diode has an exponential voltage

**/**current

__characteristic__that gives an effective " knee " voltage sometimes used as

**a**voltage reference

**.**

Any and n

__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

**.**

__Any__symmetry group whose elements have

**a**common fixed point, which

**is**true for all finite symmetry groups and also for

**the**symmetry groups

**of**bounded figures, can be represented as

**a**subgroup

**of**orthogonal group O

**(**

__n__) by choosing

**the**origin to be

**a**fixed point

**.**

__Any__rotation matrix

**of**size

__n__×

__n__can be constructed as

**a**product

**of**at most

__n__

**(**

__n__− 1 )/ 2 such rotations

**.**

To show that U

**(**__n__)**is**connected, recall that any unitary matrix A can be diagonalized by another unitary matrix S**.**__Any__diagonal unitary matrix must have complex numbers**of**absolute value 1 on**the**main diagonal**.**
for some p between 1 and

__n__**.**__Any__two such expressions**of**q**(**at**the****same**point m**of**M ) will have**the****same**number p**of**positive signs**.*******

__Any__positive multiple

**of**

**the**repunit R < sub >

__n__</ sub >< sup >( b )</ sup > contains at least

__n__nonzero digits

**in**base b

**.**

__Any__covering space

**of**

**a**differentiable manifold may be equipped with

**a**

**(**natural ) differentiable structure that turns p

**(**

**the**covering map

**in**question ) into

**a**local diffeomorphism –

**a**map with constant rank

__n__

**.**

__Any__

__n__×

__n__real symmetric matrix A determines

**a**quadratic form q < sub > A </ sub >

**in**

__n__variables by

**the**formula

0.336 seconds.