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This ring is the endomorphism ring of A. Conversely, every ring ( with identity ) is the endomorphism ring of some object in some preadditive category.

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## Some Related Sentences

ring and is

Our new large-package

__ring__twister for glass fiber yarns__is__performing well**in**our customers' mills**.**
If you walk into

**the**__ring__because it__is__fun to show your dog**,**he will feel it and give you a good performance!!
`` The reason you are

**in****the**__ring__today__is__to show your ability to present to any judge**the**most attractive picture**of**your dog that**the**skillful use**of**your aids can produce**.****This**

__is__

**the**tale

**of**one John Enright

**,**an American who has accidentally killed a man

**in**

**the**prize

__ring__and

__is__now trying to forget about it

**in**a quiet place where he may become a quiet man

**.**

`` He has married me

**with**a__ring__**of**bright water ''**,**begins**the**Kathleen Raine poem from which Maxwell takes his title**,**and it__is__this mystic bond between**the**human and natural world that**the**author conveys**.**
Many theorems which are provable using choice are

**of**an elegant general character:**every**ideal**in**a__ring____is__contained**in**a maximal ideal**,****every**vector space has a basis**,**and**every**product**of**compact spaces__is__compact**.**
The field F

__is__algebraically closed if and only if**the**only irreducible polynomials**in****the**polynomial__ring__F are those**of**degree one**.**
The ceremony

**of**such a blessing__is__similar**in****some**aspects to**the**consecration**of**a bishop**,****with****the**new abbot being presented**with****the**mitre**,****the**__ring__**,**and**the**crosier as symbols**of**office and receiving**the**laying on**of**hands and blessing from**the**celebrant**.**
The sum

**,**difference**,**product and quotient**of**two algebraic numbers__is__again algebraic**(**this fact can be demonstrated using**the**resultant ), and**the**algebraic numbers therefore form a field**,**sometimes denoted by**A****(**which may also denote**the**adele__ring__**)**or < span style =" text-decoration: overline ;"> Q </ span >.
If K

__is__a number field**,**its__ring__**of**integers__is__**the**subring**of**algebraic integers**in**K**,**and__is__frequently denoted as O < sub > K </ sub >.
In

**the**context**of**abstract algebra**,**for example**,**a mathematical**object**__is__an algebraic structure such as a group**,**__ring__**,**or vector space**.**
The configuration

**of**six carbon atoms**in**aromatic compounds__is__known as a benzene__ring__**,**after**the**simplest possible such hydrocarbon**,**benzene**.**
The structure

__is__also illustrated as a circle around**the**inside**of****the**__ring__to show six electrons floating around**in**delocalized molecular orbitals**the**size**of****the**__ring__itself**.**
In aromatic substitution one substituent on

**the**arene__ring__**,**usually hydrogen**,**__is__replaced by another substituent**.**
When there

__is__more than one substituent present on**the**__ring__**,**their spatial relationship becomes important for which**the**arene substitution patterns ortho**,**meta**,**and para are devised**.****This**

__is__seen

**in**

**,**for example

**,**phenol

**(**C < sub > 6 </ sub > H < sub > 5 </ sub >- OH ), which

__is__acidic at

**the**hydroxyl

**(**OH ), since a charge on this oxygen

**(**alkoxide-O < sup >–</ sup >)

__is__partially delocalized into

**the**benzene

__ring__

**.**

ring and endomorphism

* Given an R-module M

**,****the**__endomorphism____ring__**of**M**,**denoted End < sub > R </ sub >( M**)****is**an R-algebra by defining**(**r · φ )( x**)**= r · φ**(**x ).
In general

**,**if R**is**a__ring__and S**is**a simple module over R**,**then**,**by Schur's lemma**,****the**__endomorphism____ring__**of**S**is**a division__ring__;**every**division__ring__arises**in**this fashion from**some**simple module**.**
In

**the**case when**the**__endomorphism____ring__**,**where each__endomorphism__arises as left multiplication by a fixed__ring__element**.**
If a

**is**an idempotent**of****the**__endomorphism____ring__End < sub > R </ sub >( M ), then**the**__endomorphism__**is**an R module involution**of**M**.**That**is****,**f**is**an R homomorphism such that f < sup > 2 </ sup >**is****the****identity**__endomorphism__**of**M**.**
For example

**,****the**Fitting lemma shows that**the**__endomorphism____ring__**of**a finite length indecomposable module**is**a local__ring__**,**so that**the**strong Krull-Schmidt theorem holds and**the****category****of**finite length modules**is**a Krull-Schmidt**category****.**
Focusing on a single

**object****A****in**a**preadditive****category****,**these facts say that**the**__endomorphism__hom-set Hom**(****A****,****A****)****is**a__ring__**,**if we define multiplication**in****the**__ring__to be composition**.**

ring and .

In

**the**brief moment I had to talk to them before I took my post on**the**__ring__**of**defenses**,**I indicated I was sickened by**the**methods men employed to live and trade on**the**river__.__
For a blood-chilling

__ring__**of**terror to**the**very sound**of**his name was**the**tool he needed for**the**job he'd promised to do__.__
Opposite

**every**gate was a hitching post or a stone carriage-step**,**set**with**a rusty iron__ring__for tying a horse__.__
When they were first written

**,**there was evidently no thought**of**their being published**,**and those which refer to**the**writer's love for Mrs. Meynell particularly have**the**__ring__**of**truth__.__
Both abolition

**of**war and new techniques**of**production**,**particularly robot factories**,**greatly increase**the**world's wealth**,**a situation described**in****the**following passage**,**which has**the**true utopian__ring__: `` Everything was so cheap that**the**necessities**of**life were free**,**provided as a public service by**the**community**,**as roads**,**water**,**street lighting and drainage had once been__.__
Her mother

**,**now dead**,**was my good friend and when she came to tell us about her plans and to show off her__ring__I had a sobering wish to say something meaningful to her**,**something her mother would wish said__.__
One means to help

**the**birds occurs to me: Let**the**chimes that__ring__over Washington Square twice daily**,**discontinue any piece**of**music but one__.__
Hearing his voice

__ring__raucously up from**the**road**,**Kate would await him anxiously and watch perplexed as he walked into**the**house**,**cold sober__.__
The morning hawk

**,**hungry for any eatable**,**killable**,**digestible item**,**kept his eyes on**the**__ring__**of**anchored ships that lay off**the**shores**in****the**bay**,**sheltered by**the**Jersey inlets__.__
When you and your dog step into

**the**Junior__ring__**,**it should be just what**the**dog wants to do as much as what you want him to do__.__
Before

**the**Juniors entered**the**__ring__**the**Steward announced that after all Juniors had moved their dogs around**the**__ring__and set them up**,**they could relax**with**their dogs__.__
As

**the**Juniors entered**the**__ring__**,**Mr. Spring**,****the**announcer**,**stated over**the**public-address system that this was**the**28th year that Westminster has held**the**Finals**of****the**Junior Competition__.__
After

**the**judge moved all**the**dogs individually**,**she selected several from**the**group and placed them**in****the**center**of****the**__ring____.__
When directions read `` sl a marker on needle ''

**,**put a small safety pin**,**paper clip**,**or commercial__ring__marker on needle__.__
The energy received by

**the**`` pill '' causes**the**resonant circuit to ``__ring__'' on after**the**burst and this `` ringing '' takes place at**the**resonant frequency**of****the**`` pill ''__.__**This**gave her an opportunity to

__ring__down

**the**curtain

**with**

**the**petulant admonition that we should not presume to lecture her on Abstraction

__.__

**(**Jelke later served 21 months when he was found guilty

**of**masterminding a

__ring__

**of**high-priced call girls

__.__

Houston police got to know Diane two years ago when

**the**vice squad picked her up for questioning about a call girl__ring____.__
-- Vital secrets

**of**Britain's first atomic submarine**,****the**Dreadnought**,**and**,**by implication**,****of****the**entire United States navy's still-building nuclear sub fleet**,**were stolen by a London-based soviet spy__ring__**,**secret service agents testified today__.__
Just how many sub secrets were being handed over when

**the**__ring__**,**watched for six months**,**was broken remained untold__.__0.071 seconds.