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* Every irreducible polynomial in K which has a root in L factors into linear factors in L.

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## Some Related Sentences

Every and irreducible

__Every__

**polynomial**

**in**can be factorized

**into**polynomials that are

__irreducible__over F

**.**This factorization is unique up to permutation of the

**factors**and the multiplication of the

**factors**by nonzero constants from F ( because the ring of polynomials over

**a**field is

**a**unique factorization domain whose units are the nonzero constant polynomials ).

__Every__Heyting algebra with exactly one coatom is subdirectly

__irreducible__, whence every Heyting algebra can be made an SI by adjoining

**a**new top

**.**

*****

__Every__

__irreducible__closed subset of P < sup > n </ sup >( k ) of codimension one is

**a**hypersurface ; i

**.**e., the zero set of some homogeneous

**polynomial**

**.**

Every and polynomial

__Every__output of an encoder can be described by its own transfer function,

**which**is closely related to the generator

__polynomial__

**.**

*****

__Every__

**root**of

**a**monic

__polynomial__whose coefficients are algebraic integers is itself an algebraic integer

**.**

__Every__delta operator '

**has**

**a**unique sequence of " basic polynomials ",

**a**

__polynomial__sequence defined by three conditions:

*****

__Every__Jacobi-like

__polynomial__sequence can have its domain shifted and / or scaled so that its interval of orthogonality is, and

**has**Q

*****

__Every__Laguerre-like

__polynomial__sequence can have its domain shifted, scaled, and / or reflected so that its interval of orthogonality is, and

**has**Q =

*****

__Every__Hermite-like

__polynomial__sequence can have its domain shifted and / or scaled so that its interval of orthogonality is, and

**has**Q

__Every__field and every

__polynomial__ring over

**a**field (

**in**arbitrarily many variables ) is

**a**reduced ring

**.**

In mathematics, an integer-valued

__polynomial__( also known as**a**numerical__polynomial__) P ( t ) is**a**__polynomial__whose value P ( n ) is an integer for every integer n**.**__Every____polynomial__with integer coefficients is integer-valued, but the converse is not true**.**

Every and K

__Every__adult citizen of this small settlement signed the small petition ; E

**.**

__K__Dyer and his wife, William Johnson, Joseph Otis and his wife, Hiram Walker and his wife, Joseph Pease and R

**.**H

**.**Valentine

**.**

In November 2006, Korean singer

__K__included**a**cover of the Vandross song "__Every__Year,__Every__Christmas " on his Christmas single, ファースト ・ クリスマス (" First Christmas "), released**in**Japan**.*******

__Every__real algebraic number field

__K__of degree n contains

**a**PV number of degree n

**.**This number is

**a**field generator

**.**

This is up to isomorphism the only indecomposable module over R

**.**__Every__left R-module is**a**direct sum of ( finitely or infinitely many ) copies of this module__K__< sup > n </ sup >.*****Let

__K__< sup >

**a**</ sup > be an algebraic closure of

__K__containing

**L**

**.**

__Every__embedding σ of

**L**

**in**

__K__< sup >

**a**</ sup >

**which**restricts to the identity on

__K__, satisfies σ (

**L**) =

**L**

**.**In other words, σ is an automorphism of

**L**over

__K__

**.**

Consider

**a**Lie algebra g over**a**field__K__**.**__Every__element x of g defines the adjoint endomorphism ad ( x ) ( also written as ad < sub > x </ sub >) of g with the help of the Lie bracket, as*****

__Every__finite p-local spectrum X

**has**the property that

__K__( n )< sub >∗</ sub >( X ) = 0 if and only if n is less than

**a**certain number N, called the type of the spectrum X

**.**

( 3 )

__Every__unitary representation of G that**has**an ( ε,__K__)- invariant unit vector for any ε > 0 and any compact subset__K__,**has****a**non-zero invariant vector**.**
Soon after, the band recorded three songs at

**a**friend's rehearsal space ; the energetic tracks found early airplay on local radio and by KROQ's Rodney Bingenheimer**in****L****.**A**.**As their music further filtered across to the U**.**__K__**.**and Radio One,__Every__Move**a**Picture could be found opening hometown shows for the likes of the Kaiser Chiefs and Louis XIV**.**
Before any official release appeared overseas,

__Every__Move**a**Picture played their first U**.**__K__**.**gigs to overwhelming response**.*******25 Ta Life, 100 Demons, A Life Once Lost, A Thousand Falling Skies, The Acacia Strain, Adelphi, Agnostic Front, The A

**.**

__K__

**.**A

**.**s, Alexisonfire, All Else Failed, All That Remains, Andrew W

**.**

__K__., Anterrabae, As I Lay Dying, The Ataris, The Autumn Offering, Avail, Bad Luck 13 Riot Extravaganza, Bane, The Banner, Bear Vs

**.**Shark, Beloved, Between The Buried And Me, BigWig, Blacklisted, Bleeding Through, Blood for Blood, Breath of Silence, Brokeneck, The Bronx, Burnt by the Sun, Caliban, The Calico System, Champion, Comeback Kid, Converge, Day of Contempt, The Dead Season, Dead to Fall, Death by Stereo, XdeathstarX, Death Threat, The Dillinger Escape Plan, Draw Blood, DRI, Drive Without, Drowingman, Dry Kill Logic, E-Town Concrete, Embrace Today, Endwell, Engineer, Ensign, Evergreen Terrace,

__Every__Time I Die, Fear Before the March of Flames, Fear Factory, Flat Earth Society, Folly, For the Love of, Fordirelifesake, Forever is Forgotten, From

**a**Second Story Window, Found Dead Hanging, Full Blown Chaos, Glasseater, Halifax, Hawthorne Heights, The Hope Conspiracy, HORSE the Band, If Hope Dies, I Killed The Prom Queen, In Flames, It Dies Today, The Judas Cradle, The Juliana Theory, The Killing, Killswitch Engage, Last Perfection, Let It Die, Life of Agony, Love is Red, Malice Afterthought, Martyr AD, Mastodon, Merauder, Mest, The Minor Times, Misery Signals, Misfits, Misery Index, Most Precious Blood, Nag Hamadi, No Hollywood Ending, No Redeeming Social Value, No Warning, NORA, Norma Jean, Nothing Left to Mourn, The Number Twelve Looks Like You, Odd Project, Only Crime, Park, Pig Destroyer, Planes Mistaken for Stars, Prayer for Cleansing, Premonitions of War, The Promise, Psyopus, The Red Chord, Reflux, Remembering Never, Roses are Red, Scars of Tomorrow, Shadows Fall, Shai Hulud, Shattered Realm, Sick of it All, Spitalfield, Stabbed by Words, Stars Turn Cold, Stretch Arm Strong, Strike Anywhere, Suffocate Faster, Suffocation, Sworn Enemy, Sycamore Dreams, Terror, Time

**in**Malta, To The Grave, Today Is The Day, Through the Discipline, Throwdown, Underoath, Undying, Unearth, Until The End, Walk the Line, Walls of Jericho, Wings of Scarlet, With Dead Hands Rising, With Honor, World Inferno Friendship Society, Your Enemies Friends, Zao, Zombie Apocalypse

In mathematics,

**a**quaternion algebra over**a**field F is**a**central simple algebra A over F that**has**dimension 4 over F**.**__Every__quaternion algebra becomes the matrix algebra by extending scalars (= tensoring with**a**field extension ), i**.**e**.**for**a**suitable field extension__K__of F, is isomorphic to the 2 × 2 matrix algebra over__K__**.**

Every and which

__Every__new scandal

__which__would provide more `` copy '' for Marshall's pen would thus mean more publicity for Welch

**.**

__Every__dream, and this is true of

**a**mental image of any type even though it may be readily interpreted

**into**its equivalent of wakeful thought, is

**a**psychic phenomenon for

__which__no explanation is available

**.**

__Every__family of Riviera Presbyterian Church

**has**been asked to read the Bible and pray together daily during National Christian Family Week and to undertake one project

**in**

__which__all members of the family participate

**.**

** Zorn's lemma:

__Every__non-empty partially ordered set**in**__which__every chain ( i**.**e**.**totally ordered subset )**has**an upper bound contains at least one maximal element**.*******

__Every__continuous functor on

**a**small-complete category

__which__satisfies the appropriate solution set condition

**has**

**a**left-adjoint ( the Freyd adjoint functor theorem ).

__Every__telephone company, whether large or small, determines its own ANAC for each individual central office,

__which__tends to perpetuate the current situation of

**a**mess of overlapping and / or spotty areas of coverage

**.**

__Every__field

**has**an algebraic extension

__which__is algebraically closed ( called its algebraic closure ), but proving this

**in**general requires some form of the axiom of choice

**.**

__Every__year since 1972 the BVI

**has**hosted the Spring Regatta,

__which__is

**a**seven-day collection of sailing races throughout the islands

**.**

*****

__Every__real Banach algebra

__which__is

**a**division algebra is isomorphic to the reals, the complexes, or the quaternions

**.**

*****

__Every__unital real Banach algebra with no zero divisors, and

**in**

__which__every principal ideal is closed, is isomorphic to the reals, the complexes, or the quaternions

**.**

__Every__character is automatically continuous from A to C, since the kernel of

**a**character is

**a**maximal ideal,

__which__is closed

**.**

__Every__computer contains an internal clock that regulates the rate at

__which__instructions are executed and synchronizes all the various computer components

**.**

*****Duality:

__Every__statement, theorem, or definition

**in**category theory

**has**

**a**dual

__which__is essentially obtained by " reversing all the arrows ".

__Every__context-sensitive grammar

__which__does not generate the empty string can be transformed

**into**an equivalent one

**in**Kuroda normal form

**.**

According to

__Every__, one example may be " the myth of St**.**George " and other stories about saints battling dragons,__which__were " modelled no doubt**in**many cases on older representations of the creator and preserver of the world**in**combat with chaos ".__Every__argues that " the disparagement of myth

**in**our own civilization " stems partly from objections to perceived idolatry, objections

__which__intensified

**in**the Reformation, both among Protestants and among Catholics reacting against the classical mythology revived during the Renaissance

**.**

__Every__grammar

**in**Chomsky normal form is context-free, and conversely, every context-free grammar can be transformed

**into**an equivalent one

__which__is

**in**Chomsky normal form

**.**

__Every__four years, during

__which__an extra 24 hours have accumulated, one extra day is added to keep the count coordinated with the sun's apparent position

**.**

__Every__sequence can, thus, be read

**in**three reading frames, each of

__which__will produce

**a**different amino acid sequence (

**in**the given example, Gly-Lys-Pro, Gly-Asn, or Glu-Thr, respectively ).

__Every__time the boy had an injury

__which__caused him internal or external bleeding, the Tsarina called on Rasputin, and the Tsarevich subsequently got better

**.**

__Every__week before June 19, the strip focuses on Garfield's birthday,

__which__he dreads because of his fear of getting older

**.**

:::

__Every__Bill__which__shall have passed the House of Representatives and the Senate, shall, before it become**a**Law, be presented to the President of the United States ; If he approves he shall sign it, but if not he shall return it, with his Objections to that House**in**__which__it shall have originated ...0.544 seconds.