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* Every left ideal I in R is finitely generated, i. e. there exist elements a < sub > 1 </ sub >, ..., a < sub > n </ sub > in I such that I = Ra < sub > 1 </ sub > + ... + Ra < sub > n </ sub >.

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## Some Related Sentences

Every and left

__Every__January 19

**,**

**in**the early hours of the morning

**,**the person made

**a**toast of cognac to Poe's original grave marker and

__left__three roses

**.**

If the book itself

**,**Animal Farm**,**had__left__any doubt of the matter**,**Orwell dispelled it**in**his essay Why**I**Write: '__Every__line of serious work**that****I**’ ve written since 1936 has been written directly or indirectly against Totalitarianism**...**dot**,**dot**,**dot**,**dot**.**__Every__topological group can be viewed as

**a**uniform space

**in**two ways ; the

__left__uniformity turns all

__left__multiplications into uniformly continuous maps while the right uniformity turns all right multiplications into uniformly continuous maps

**.**

*****

__Every__non-empty set of

__left__ideals of

**R**

**,**partially ordered by inclusion

**,**has

**a**maximal element with respect to set inclusion

**.**

__Every__one of the features encompassed by the theory still requires

**a**reason for it to be maintained after hominids

__left__the aquatic environment

**.**

__Every__year since 1880

**,**the organizations of the French

__left__have held

**a**demonstration

**in**this symbolic place during the last week of May

**.**

"

__Every__part of his body has been replaced**,**with the exception of " all the diodes down__left__side ," which have been giving him severe pain for the whole of his existence**.**__Every__actor provided multiple voices

**,**although the distinctive baritone of Earle Hyman ( Panthro )

__left__the actor providing only very occasional guest voices

**in**comparison with his fellow performers

**.**

__Every__factual error

__left__

**in**the published records

**is**officially considered to be

**a**failure by the responsible officer

**.**

__Every__week

**,**he

__left__her food near the statue

**,**which was placed outside the house

**,**but nobody knew he was doing it

**.**

__Every__seat

**in**the ballpark

**is**green

**,**except for two-one

**in**

__left__field which marks the spot of Cal Ripken's 278th career homerun

**,**breaking Ernie Banks'all time record among shortstops

**,**and one

**in**right field

**,**which marks the spot of Eddie Murray's 500th career homerun

**.**

__Every__chain either has the middle tile on the outside ( O ) or the inside (

**I**) of the chain ; if it

**is**arranged so

**that**the indicator tile

**is**to the right of the middle tile

**,**then the position of the ring segment on the indicator tile can either be the upper

__left__( UL ), upper right ( UR ), lower

__left__( LL ) or lower right ( LR ) corner

**.**

__Every__day

**,**she saw trucks loaded with Jews heading to the railway station from where the trains

__left__for concentration camps

**.**

__Every__member of the Queen's Royal Hussars of the United Kingdom light cavalry wears the Maid of Warsaw

**,**the crest of the City of Warsaw

**,**on the

__left__sleeve of his No

**.**2 ( Service ) Dress

**.**

__Every__Samhain

**,**the phantom Aillén mac Midgna

**,**or Aillén the Burner

**,**would terrorize Tara

**,**playing music on his harp

**that**

__left__every warrior helpless

**.**

Every and ideal

*****

__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

**.**

*****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__**finitely****generated**__ideal__of A**is**principal (**i****.****e**., A**is****a**Bézout domain ) and A satisfies the ascending chain condition on principal ideals**.**__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__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__field of either type can be realized as the field of fractions of

**a**Dedekind domain

**in**which every non-zero

__ideal__

**is**of finite index

**.**

In Leedskalnin's own publication A Book

**in**__Every__Home he implies his " Sweet Sixteen " was more an__ideal__than**a**reality**.**__Every__meal can be eaten without any cooking ; when circumstances permit

**,**the

__ideal__method of preparation

**is**to cook the entrees

**in**

**a**pressure cooker

**,**heated on the standard issue Coleman stove

**,**or by simply boiling the rations

**in**its package

**in**water

**.**

__Every__free spirit looked upon her as protectoress and

__ideal__.... Marguerite was the embodiment of charity

**.**

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