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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.

from
Wikipedia

## Some Related Sentences

Every and simple

#

__Every____simple__path from**a**given node**to****any****of**its descendant leaves contains**the**same number**of**black nodes**.**
" I might easily have written this story in

**the**traditional manner [...]__Every__novelist knows**the**recipe [...] It**is**not very difficult**to**follow**a**__simple__**,**chronological scheme which**the**critics will understand [...] But I**,**after all**,**am trying**to**tell**the**story**of**this Chapelizod family in**a**new way**.**__Every__October

**,**Moriarty plays host

**to**

**the**Pinto Bean Fiesta

**,**which

**is**composed

**of**

**a**bunch

**of**

__simple__games in Crossly Park

**,**as well as

**a**parade and crowning

**of**

**a**" Pinto Bean Queen

**.**

__Every__one

**of**

**the**infinitely many vertices

**of**G can be reached from v < sub > 1 </ sub > with

**a**

__simple__path

**,**and each such path must start with one

**of**

**the**finitely many vertices adjacent

**to**v < sub > 1 </ sub >.

__Every__hour that Napoleon could have attacked earlier as he did

**,**would have been

**is**his favour

**,**but

**the**French could not attack in

**the**morning for

**the**

__simple__reason that

**the**entire army had not yet taken its battle positions

**.**

__Every__closed curve c on X

**is**homologous

**to**for some

__simple__closed curves c < sub > i </ sub >, that

**is**

**,**

*

__Every__finite-dimensional__simple__algebra over**R**must be**a**matrix ring over**R****,**C**,**or H**.**__Every__central__simple__algebra over**R**must be**a**matrix ring over**R**or H**.**These results follow from**the**Frobenius theorem**.**
*

__Every__finite-dimensional__simple__algebra over C must be**a**matrix ring over C and hence every central__simple__algebra over C must be**a**matrix ring over C**.**
*

__Every__finite-dimensional central__simple__algebra over**a**finite field must be**a**matrix ring over that field**.**
*

__Every__automorphism**of****a**central__simple__algebra**is**an inner automorphism ( follows from Skolem – Noether theorem ).
*

__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**.**
# Personal

**right**:__Every__person has**a****right****to**life but this**right****is**restricted and has attached certain duties –__simple__living**is**essential**.**__Every__Sámi settlement had its seita

**,**which had no regular shape

**,**and might consist

**of**smooth or odd-looking stones picked out

**of**

**a**stream

**,**

**of**

**a**small pile

**of**stones

**,**

**of**

**a**tree-stump

**,**or

**of**

**a**

__simple__post

**.**

Every and R-module

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 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

**.**

Every and isomorphic

*

__Every__real Banach algebra which**is****a**division algebra**is**__isomorphic__**to****the**reals**,****the**complexes**,**or**the**quaternions**.**
*

__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__commutative real unital Noetherian Banach algebra with no zero divisors**is**__isomorphic__**to****the**real or complex numbers**.**__Every__well-ordered set

**is**uniquely order

__isomorphic__

**to**

**a**unique ordinal number

**,**called

**the**order type

**of**

**the**well-ordered set

**.**

__Every__finite-dimensional vector space

**is**

__isomorphic__

**to**its dual space

**,**but this isomorphism relies on an arbitrary choice

**of**isomorphism ( for example

**,**via choosing

**a**basis and then taking

**the**isomorphism sending this basis

**to**

**the**corresponding dual basis ).

__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__universal cover p: D → X

**is**regular

**,**with deck transformation group being

__isomorphic__

**to**

**the**fundamental group

**.**

__Every__Riemann surface

**is**

**the**

**quotient**

**of**

**a**free

**,**proper and holomorphic action

**of**

**a**discrete group on its universal covering and this universal covering

**is**holomorphically

__isomorphic__( one also says: " conformally equivalent ")

**to**one

**of**

**the**following:

Iwasawa worked with so-called-extensions: infinite extensions

**of****a**number field with Galois group__isomorphic__**to****the**additive group**of**p-adic integers for some prime p**.**__Every__closed subgroup**of****is****of****the**form**,**so by Galois theory**,**a-extension**is****the**same thing as**a**tower**of**fields such that**.**
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__Calabi – Yau manifold in 4 ( real ) dimensions**is****a**hyperkähler manifold**,**because SU ( 2 )**is**__isomorphic__**to**Sp ( 1 ).
Also

**,****a**kind**of**converse holds:__Every__algebraic lattice**is**__isomorphic__**to**Sub ( A ) for some algebra A**.**
A finitely-generated abelian group

**is**indecomposable if and only if it**is**__isomorphic__**to**Z or**to****a**factor group**of****the**form for some prime number p and some positive integer n**.**__Every__finitely-generated abelian group**is****a**direct sum**of**( finitely many ) indecomposable abelian groups**.**__Every__( normal ) Boolean algebra with operators can be represented as

**a**field

**of**sets on

**a**relational structure in

**the**sense that it

**is**

__isomorphic__

**to**

**the**complex algebra corresponding

**to**

**the**field

**.**

__Every__commutative von Neumann algebra on

**a**separable Hilbert space

**is**

__isomorphic__

**to**L < sup >∞</ sup >( X ) for some standard measure space ( X

**,**μ ) and conversely

**,**for every standard measure space X

**,**L < sup >∞</ sup >( X )

**is**

**a**von Neumann algebra

**.**

In mathematics

**,****a**quaternion algebra over**a**field F**is****a**central**simple**algebra A over F that has dimension 4 over F**.**__Every__quaternion algebra becomes**the**matrix algebra by extending scalars (= tensoring with**a**field extension ), i**.**e**.**for**a**suitable field extension K**of**F**,****is**__isomorphic__**to****the**2 × 2 matrix algebra over K**.**0.323 seconds.