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Every simple module is cyclic, that is it is generated by one element.

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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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