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Every finite-length module M has a composition series, and the length of every such composition series is equal to the length of M.

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## Some Related Sentences

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__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__

**.**

__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__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 M

* In any ring R

**,****a**maximal ideal**is**an ideal__M__that**is**maximal in**the**set**of**all proper ideals**of**R**,**i**.**e**.**__M__**is**contained in exactly 2 ideals**of**R**,**namely__M__itself**and****the**entire ring R**.**__Every__maximal ideal**is**in fact prime**.**__Every__smooth ( or differentiable ) map φ:

__M__→ N between smooth ( or differentiable ) manifolds induces natural linear maps between

**the**corresponding tangent spaces:

__Every__measurable cardinal κ

**is**

**a**0-huge cardinal because < sup > κ </ sup >

__M__⊂

__M__

**,**that

**is**

**,**

**every**function from κ

**to**

__M__

**is**in

__M__

**.**Consequently

**,**V < sub > κ + 1 </ sub >⊂

__M__

**.**

:

__Every__countable theory which**is**satisfiable in**a**model__M__**,****is**satisfiable in**a**countable substructure**of**__M__**.**
* Siegal

**,**__M__., Cornell Feline Health Center ( Editors ) ( 1989 ) The Cornell Book**of**Cats: A Comprehensive Medical Reference for__Every__Cat**and**Kitten**.**__Every__year about 5000 applications are received

**,**out

**of**which about 300 students ( around 150 in each year ) are enrolled in

**the**2 year full time

__M__

**.**Tech

**.**

__Every__hyperkähler manifold

__M__

**has**

**a**2-sphere

**of**complex structures ( i

**.**e

**.**integrable almost complex structures ) with respect

**to**which

**the**metric

**is**Kähler

**.**

*

__Every__direct summand**of**__M__**is**pure in__M__**.**Consequently**,****every**subspace**of****a**vector space over**a**field**is**pure**.**

Every and has

__Every__woman

__has__had

**the**experience

**of**saying no when she meant yes

**,**

**and**saying yes when she meant no

**.**

__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__family

**of**Riviera Presbyterian Church

__has__been asked

**to**read

**the**Bible

**and**pray together daily during National Christian Family Week

**and**

**to**undertake one project in which all members

**of**

**the**family participate

**.**

__Every__community

**,**if it

**is**alive

__has__

**a**spirit

**,**

**and**that spirit

**is**

**the**center

**of**its unity

**and**identity

**.**

__Every__

**such**subset

__has__

**a**smallest element

**,**so

**to**specify our choice function we can simply say that it maps each set

**to**

**the**least element

**of**that set

**.**

** Zorn's lemma:

__Every__non-empty partially ordered set in which**every**chain ( i**.**e**.**totally ordered subset )__has__an upper bound contains at least one maximal element**.**
The restricted principle "

__Every__partially ordered set__has__**a**maximal totally ordered subset "**is**also equivalent**to**AC over ZF**.**
** Tukey's lemma:

__Every__non-empty collection**of**finite character__has__**a**maximal element with respect**to**inclusion**.**
*

__Every__continuous functor on**a**small-complete category which satisfies**the**appropriate solution set condition__has__**a**left-adjoint (**the**Freyd adjoint functor theorem ).__Every__unit

**of**

**length**

__has__

**a**corresponding unit

**of**area

**,**namely

**the**area

**of**

**a**square with

**the**given side

**length**

**.**

__Every__field

__has__an algebraic extension which

**is**algebraically closed ( called its algebraic closure ), but proving this in general requires some form

**of**

**the**axiom

**of**choice

**.**

__Every__ATM cell

__has__an 8-or 12-bit Virtual Path Identifier ( VPI )

**and**16-bit Virtual Channel Identifier ( VCI ) pair defined in its header

**.**

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