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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.

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## Some Related Sentences

Every and module

__Every__library

__module__

**has**at least two source files:

**a**definitions file specifying

**the**library's interface plus one or more program files specifying

**the**implementation of

**the**procedures in

**the**interface

**.**

__Every__simple R-module is isomorphic to

**a**quotient R / m where m is

**a**maximal right ideal of R

**.**By

**the**above paragraph

**,**any quotient R / m is

**a**simple

__module__

**.**

__Every__vector space is free

**,**

**and**

**the**free vector space on

**a**set is

**a**special case of

**a**free

__module__on

**a**set

**.**

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 >.__Every__finite-length

__module__M

**has**

**a**composition series

**,**

**and**

**the**length of every such composition series is equal to

**the**length of M

**.**

__Every__

**ring**which is semisimple as

**a**

__module__

**over**itself

**has**zero Jacobson radical

**,**but not every

**ring**with zero Jacobson radical is semisimple as

**a**

__module__

**over**itself

**.**

__Every__superfield

**,**i

**.**e

**.**

**a**field that depends on all coordinates of

**the**superspace ( or in other words

**,**an element of

**a**

__module__of

**the**algebra of functions

**over**superspace ), may

**be**expanded with respect to

**the**new fermionic coordinates

**.**

Every and over

The restricted principle "

__Every__partially ordered set**has****a**maximal totally ordered subset " is also equivalent to AC__over__ZF**.**__Every__six months

**the**presidency rotates

**between**

**the**states

**,**in an order predefined

**by**

**the**Council's members

**,**allowing each state to preside

__over__

**the**body

**.**

*

__Every__June**,**Ellensburg hosts Dachshunds on Parade**,**an event that draws Dachshund dog owners from all__over__**the**Northwest**.**__Every__year sidecar racers travel from all

__over__

**the**UK to Knockhill in Scotland to race in

**the**prestigious ' Jock Taylor Memorial Trophy ' race

**.**

__Every__major commercial transport

**and**almost every military jet built in

**the**United States

__over__

**the**last 40 years

**has**been tested in this facility

**.**

__Every__car uses either

**a**5

**.**0 L Ford " Boss 302 " SVO or

**a**5

**.**0 L Chevrolet small block race-engine ( depending on

**the**make )-capable of producing

**between**460

**and**485 kW ( 620 — 650 bhp ) of power

**,**but generally quoted as

**a**little

__over__450 kW ( 600 bhp ) in race trim

**.**

__Every__character in

**the**novel — both men

**and**women — knows their place

**,**

**and**

**the**traditional stereotypes of gender roles are repeated

__over__

**and**

__over__again

**.**

__Every__Turing machine computes

**a**certain fixed partial computable function from

**the**input strings

__over__its alphabet

**.**

__Every__Calan Mai

**,**

**the**two would fight

__over__Creiddylad

**,**until

**a**battle on Judgement Day

**,**in which

**the**victor would keep her forever

**.**

Controversy ensued

__over__**the**use of**the**phrase "__Every__seat lost to**the**government is**a**seat sold to**the**Boers " as**the**Unionists waged**a**personalised campaign against Liberal critics of**the**war – some posters even portrayed Liberal MPs praising President Kruger**and**helping him to haul down**the**Union Jack**.**__Every__year

**,**

**the**post office also creates

**a**special Christmas hand-cancellation pictorial postmark for use during December

**,**which also attracts mail from all

__over__

**the**world

**.**

A quotation attributed to Kolmogorov is into English: "

__Every__mathematician believes that he is ahead__over__all others**.**__Every__August

**the**Mountain Mama Road Bike Challenge brings cyclists from all

__over__

**the**country to challenge themselves on

**the**steep roads of Highland County

**.**

The argument

__over__**the**quality of Fitzgerald ’ s translation of**the**Rubaiyat**has****,**according to Dougan**,**diverted attention from**a**fuller understanding of**the**deeply esoteric message contained in Omar ’ s actual material – "__Every__line of**the**Rubaiyat**has**more meaning than almost anything you could read in Sufi literature ".

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__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

**.**

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