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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 >.

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## Some Related Sentences

is and up

`` Amen '', said

**the**Reverend Doran, grabbing his rifle propped__up__against**a**tombstone, `` and now my brethren, it would seem that our presence__is__required elsewhere ''**.**
It became

**the**sole `` subject ''**of**`` international law ''**(****a**term which, it__is__pertinent**to**remember, was coined by Bentham**)**,**a**body**of**legal principle which by and large was made__up__**of**what Western nations could do in**the**world arena**.**
It

__is__**the**gait**of****the**human who must run**to**live: arms dangling, legs barely swinging**over****the**ground, head hung down and**only**occasionally swinging__up__**to**see**the**target,**a**loose motion that__is__just short**of**stumbling and yet__is__wonderfully graceful**.**
On Fridays,

**the**day when**many**Persians relax with poetry, talk, and**a**samovar, people do not, it__is__true, stream into Chehel Sotun --**a**pavilion and garden built by Shah Abbas 2, in**the**seventeenth century -- but they do retire into hundreds**of**pavilions throughout**the**city and__up__**the**river valley, which are smaller, more humble**copies****of****the**former**.**
Unruly hair goes straight

__up__from his forehead, standing so high that**the**top falls gently**over**, as if**to**show that it really__is__hair and not bristle**.**
When I try

**to**work out my reasons for feeling that**this**passage__is__**of**critical significance, I come__up__with**the**following ideas, which I shall express very briefly here and revert**to**in**a**later essay**.**
Professionally

**a**lawyer, that__is__**to**say associated with dignity, reserve, discipline, with much that__is__essentially middle-class, he__is__compelled by an impossible love**to**exhibit himself dressed__up__, disguised -- that__is__, paradoxically, revealed -- as**a**child, and, worse, as**a**whore masquerading as**a**child**.**
Was it supposed, perchance, that A & M

**(**vocational training, that__is__**)**was quite sufficient for**the**immigrant class which flooded that part**of****the**New England world in**the**post-Civil War period,**the**immigrants having been brought in from Southern Europe,**to**work in**the**mills,**to**make__up__for**the**labor shortage caused by migration**to****the**West??
Presumably

**a**cocktail party__is__expected**to**fulfill**the**host's desire**to**get together**a**number**of**people who are inadequately acquainted and thereby arrange for bringing**the**level**of**acquaintance__up__**to**adequacy for future cooperative endeavors**.****This**

__is__done for simplicity

**of**commands and

**to**bring

**the**hidden redundancy

__up__

**to**where misunderstanding has almost zero possibility

**.**

A further regulation

__is__that commands always go down, unaccompanied by statements, and statements always go__up__, unaccompanied by commands**.**
It

__is__**of****the**utmost importance**to****the**people**of**America and**of****the**world how their governing President `` ends__up__'' during**the**four years**of**his term**.**
But

**a**modern Oedipus who__is__doomed because he cannot oppose his own childhood__is__**only**pathetic, and for renouncing**the**mystery in favor**of**psychological truth he gives__up__**the**claim on our sympathies**.**
`` Dear Miss Steichen: It

__is__**a**very good letter you send me -- softens**the**intensity**of****this**guerilla warfare I am carrying on__up__here**.**
Community decision makers must make

__up__their minds whether**a**claim__is__acceptable**to****the**larger community in terms**of**prevailing expectations regarding members**of**nation states**.**
but

**the**possibility**of****this**effort__is__bound__up__with that development**of**historical thought which__is__**the**greatest achievement**of**our civilization in**the**last two centuries, and it__is__utterly impossible**to**people in whom**this**development has not taken place**.**

is and isomorphism

In category theory, an automorphism

__is__an endomorphism**(**i**.**e**.****a**morphism from an object**to**itself**)**which__is__also an__isomorphism__**(**in**the**categorical sense**of****the**word ).
* Inverses: by definition every

__isomorphism__has an inverse which__is__also an__isomorphism__, and since**the**inverse__is__also an endomorphism**of****the**same object it__is__an automorphism**.**
In

**a**category with exponentials, using**the**__isomorphism__**(**in computer science,**this**__is__called currying ),**the**Ackermann function may be defined via primitive recursion**over**higher-order functionals as follows:
Using Zorn's lemma, it can be shown that every field has an algebraic closure, and that

**the**algebraic closure**of****a**field**K**__is__unique**up****to**an__isomorphism__that fixes every member**of****K****.**Because**of****this**essential uniqueness, we often speak**of****the**algebraic closure**of****K**, rather than an algebraic closure**of****K****.**
In fact, when A

__is__**a**commutative unital C *- algebra,**the**Gelfand representation__is__then an isometric *-__isomorphism__between A and C**(**Δ**(**A ))**.**
Sometimes two quite different constructions yield "

**the**same " result ;**this**__is__expressed by**a**natural__isomorphism__between**the**two functors**.**
The two functors F and G are called naturally isomorphic if there exists

**a**natural transformation from F**to**G such that η**<**sub**>**X**</**sub**>**__is__an__isomorphism__for every object X in C**.**
Bicategories are

**a**weaker notion**of**2-dimensional categories in which**the**composition**of**morphisms__is__not strictly associative, but**only**associative "**up****to**" an__isomorphism__**.**
In category theory, currying can be found in

**the**universal property**of**an exponential object, which gives rise**to****the**following adjunction in cartesian closed categories: There__is__**a**natural__isomorphism__between**the**morphisms from**a**binary product and**the**morphisms**to**an exponential object**.**

is and only

Bryn Mawr Drive

__is____only__two**or**three miles from**the**Spartan, and it took me less than five minutes**to**get there**.**
Actually,

__only__two men know what**the**formula__is__, Blake and '' -- He stopped and looked at Thor's body**.**
In fact it has caused us

**to**give serious thought**to**moving our residence south, because it__is__not easy for**the**most objective Southerner**to**sit calmly by when his host__is__telling**a**roomful**of**people that**the**__only__way**to**deal with Southerners who oppose integration__is__**to**send in troops and shoot**the**bastards down**.****This**

__is__

**the**

__only__case in modern history

**of**

**a**people

**of**Britannic origin submitting without continued struggle

**to**what they view as foreign domination

**.**

Recognizing that

**the**Rule**of**Law__is__``**a**dynamic concept which should be employed not__only__**to**safeguard**the**civil and political rights**of****the**individual in**a**free society '',**the**Congress asserted that it also included**the**responsibility ``**to**establish social, economic, educational and cultural conditions under which his legitimate aspirations and dignity may be realized ''**.**
They are huge areas which have been swept by winds for so

**many**centuries that there__is__no soil**left**, but__only__deep bare ridges fifty**or**sixty yards apart with ravines between them thirty**or**forty feet deep and**the**__only__thing that moves__is__**a**scuttling layer**of**sand**.**
Others are confined

**to**vast reservations, and not__only__does**the**Australian government justifiably not wish them**to**be viewed as exhibits in**a**zoo, but on their reservations they are extremely fugitive, shunning camps, coming together__only__for corroborees at which their strange culture comes**to**its highest pitch -- which__is__very low indeed**.**
`` Now that Bruno Walter

__is__virtually in retirement and my dear friend Dimitri Mitropoulos__is__no longer with us, I am probably**the**__only__one -- with**the**possible exception**of**Leonard Bernstein -- who has**this**special affinity for and champions**the**works**of**Bruckner and Mahler ''**.**
Thus, there

__is__freshness not__only__in**the**individual movements**of****the**dance but in**the**shape**of**their continuity as well**.**
The answers derived by these means may determine not

__only__**the**temporal organization**of****the**dance but also its spatial design, special slips designating**the**location on**the**stage where**the**movement__is__**to**be performed**.**
I think it

__is__essential, however,**to**pinpoint here**the**difference between**the**two concepts**of**sovereignty that went**to**war in 1861 -- if__only__**to**see better how imperative__is__our need today**to**clarify completely our far worse confusion on**this**subject**.**
To my knowledge, Lincoln remains

**the**__only__Head**of**State and Commander-in-Chief who, while fighting**a**fearful war whose issue was in doubt, proved man enough**to**say**this**publicly --**to**give his foe**the**benefit**of****the**fact that in all human truth there__is__some error, and in all our error, some truth**.**0.178 seconds.