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Every simple module is indecomposable, but the converse is in general not true.

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## 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**.**__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**

**.**

" 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 module

__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

**.**

__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__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 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

**.**

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