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Every division ring is therefore a division algebra over its center.

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## Some Related Sentences

Every and division

*

__Every__real Banach**algebra**which**is****a**__division__**algebra****is**isomorphic to the reals, the complexes, or the quaternions**.**__Every__corporation, whether financial or union, as well as every

__division__of the administration, were set up as branches of the party, the CEOs, Union leaders, and

__division__directors being sworn-in as section presidents of the party

**.**

__Every__module

**over**

**a**

__division__

**ring**has

**a**basis ; linear maps between finite-dimensional modules

**over**

**a**

__division__

**ring**can be described by matrices, and the Gaussian elimination algorithm remains applicable

**.**

__Every__time one levels up

**a**class

__division__, one

**is**given one extra attribute point until it reaches

__division__level 50, such that

**a**non reincarnated char has

**a**total of 236 points, 216 points the character can invest as there

**is**always 5 Tactics, Clout, Education and Mechanical Aptitude to start with

**.**

We call

**a**field E**a**splitting field for A if A ⊗ E**is**isomorphic to**a**matrix**ring****over**E**.**__Every__finite dimensional CSA has**a**splitting field: indeed, in the case when A**is****a**__division__**algebra**, then**a**maximal subfield of A**is****a**splitting field**.**
*

__Every__4-dimensional central simple**algebra****over****a**field F**is**isomorphic to**a**quaternion**algebra**; in fact, it**is**either**a**two-by-two matrix**algebra**, or**a**__division__**algebra****.**
for the purpose of sale or of building development:

__Every____division__of**a**piece of land into two or more lots, parcels or parts**is**, of course,**a**subdivision**.**__Every__year, conferences with topics pertaining to choral conductors are held-in even numbered years,

**a**

__division__conference

**is**held in each

__division__, and in odd numbered years,

**a**national conference takes place in

**a**major U

**.**S

**.**city

**.**

__Every__

__division__

**is**headed by

**a**trustee, each responsible for publishing in the languages specific to that

__division__

**.**

__Every__other NFL team played

**a**home-and-away series against the other members in

**its**

__division__, three interconference games, and the remainder of their 14 game schedule against other conference teams

**.**

__Every__other NFL team played

**a**home-and-away series against the other members in

**its**

__division__, three interconference games, and the remainder of their 14 game schedule against other conference teams

**.**

__Every__major

__division__, called

**a**thema ( Greek: θέμα ), was further divided into tourmai while each tourma was divided into moirai or droungoi, which in turn were composed of several banda

**.**

Every and ring

__Every__Boolean

**algebra**( A, ∧, ∨) gives rise to

**a**

__ring__( A, +, ·) by defining

**a**+ b := (

**a**∧ ¬ b ) ∨ ( b ∧ ¬

**a**) = (

**a**∨ b ) ∧ ¬(

**a**∧ b ) ( this operation

**is**called symmetric difference in the case of sets and XOR in the case of logic ) and

**a**· b :=

**a**∧ b

**.**The zero element of this

__ring__coincides with the 0 of the Boolean

**algebra**; the multiplicative identity element of the

__ring__

**is**the 1 of the Boolean

**algebra**

**.**

In Norse mythology, Draupnir ( Old Norse " the dripper ")

**is****a**gold__ring__possessed by the god Odin with the ability to multiply itself:__Every__ninth night eight new rings ' drip ' from Draupnir, each one of the same size and weight as the original**.**__Every__objective has

**a**different size

__ring__, so for every objective another condenser setting has to be chosen

**.**

__Every__match must be assigned

**a**rule keeper known as

**a**referee, who

**is**the final arbitrator ( In multi-man lucha libre matches, two referees are used, one inside the

__ring__and one outside ).

* In any

__ring__R,**a**maximal ideal**is**an ideal M that**is**maximal in the set of all proper ideals of R, i**.**e**.**M**is**contained in exactly 2 ideals of R, namely M itself and the entire__ring__R**.**__Every__maximal ideal**is**in fact prime**.**__Every__prime ideal P in

**a**Boolean

__ring__R

**is**maximal: the quotient

__ring__R / P

**is**an integral domain and also

**a**Boolean

__ring__, so it

**is**isomorphic to the field F < sub > 2 </ sub >, which shows the maximality of P

**.**Since maximal ideals are always prime, prime ideals and maximal ideals coincide in Boolean rings

**.**

__Every__topological

__ring__

**is**

**a**topological group ( with respect to addition ) and hence

**a**uniform space in

**a**natural manner

**.**

__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 and is

__Every__legislator from Brasstown Bald to Folkston

__is__going to have his every vote subjected to the closest scrutiny as

**a**test of his political allegiances, not his convictions

**.**

__Every__detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he

__is__playing with Viennese musicians ), and the gossamer shading throughout

**.**

__Every__taxpayer

__is__well aware of the vast size of our annual defense budget and most of our readers also realize that

**a**large portion of these expenditures go for military electronics

**.**

__Every__few days, in the early morning, as the work progressed, twenty men would appear to push it ahead and to shift the plank foundation that distributed

**its**weight widely on the Rotunda pavement, supported as it

__is__by ancient brick vaulting

**.**

__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__library borrower, or at least those whose taste goes beyond the five-cent fiction rentals, knows what it

__is__to hear the librarian say apologetically, `` I'm sorry, but we don't have that book

**.**

__Every__community, if it

__is__alive has

**a**spirit, and that spirit

__is__the

**center**of

**its**unity and identity

**.**

The restricted principle "

__Every__partially ordered set has**a**maximal totally ordered subset "__is__also equivalent to AC**over**ZF**.**__Every__natural-born citizen of

**a**foreign state who

__is__also an American citizen and every natural-born American citizen who

__is__

**a**citizen of

**a**foreign land owes

**a**double allegiance, one to the United States, and one to his homeland ( in the event of an immigrant becoming

**a**citizen of the US ), or to his adopted land ( in the event of an emigrant natural born citizen of the US becoming

**a**citizen of another nation ).

__Every__line of written text

__is__

**a**mere reflection of references from any of

**a**multitude of traditions, or, as Barthes puts it, " the text

__is__

**a**tissue of quotations drawn from the innumerable centres of culture "; it

__is__never original

**.**

__Every__year, on the last Sunday in April, there

__is__an ice fishing competition in the frozen estuarine waters of the Anadyr River's mouth

**.**

__Every__lattice element of the structure

__is__in

**its**proper place, whether it

__is__

**a**single atom or

**a**molecular grouping

**.**

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