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* Every module over a field or skew field is projective ( even free ).

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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__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 over

The restricted principle "

__Every__partially ordered set has**a**maximal totally ordered subset "**is**also equivalent to AC__over__ZF.__Every__six months the presidency rotates between the states, in an order predefined by the Council's members, allowing each state to preside

__over__the body.

*****

__Every__June, Ellensburg hosts Dachshunds on Parade, an event that draws Dachshund dog owners from all

__over__the Northwest.

__Every__year sidecar racers travel from all

__over__the UK to Knockhill in Scotland to race in the prestigious ' Jock Taylor Memorial Trophy ' race.

__Every__major commercial transport and almost every military jet built in the United States

__over__the last 40 years has been tested in this facility.

__Every__car uses either

**a**5. 0 L Ford " Boss 302 " SVO

**or**

**a**5. 0 L Chevrolet small block race-engine

**(**depending on the make )-capable of producing between 460 and 485 kW

**(**620 — 650 bhp ) of power, but generally quoted as

**a**little

__over__450 kW

**(**600 bhp ) in race trim.

__Every__character in the novel — both men and women — knows their place, and the traditional stereotypes of gender roles are repeated

__over__and

__over__again.

__Every__Turing machine computes

**a**certain fixed partial computable function from the input strings

__over__its alphabet.

__Every__Calan Mai, the two would fight

__over__Creiddylad, until

**a**battle on Judgement Day, in which the victor would keep her forever.

Controversy ensued

__over__the use of the phrase "__Every__seat lost to the government**is****a**seat sold to the Boers " as the Unionists waged**a**personalised campaign against Liberal critics of the war – some posters**even**portrayed Liberal MPs praising President Kruger and helping him to haul down the Union Jack.__Every__year, the post office also creates

**a**special Christmas hand-cancellation pictorial postmark for use during December, which also attracts mail from all

__over__the world.

A quotation attributed to Kolmogorov

**is**into English: "__Every__mathematician believes that he**is**ahead__over__all others.__Every__August the Mountain Mama Road Bike Challenge brings cyclists from all

__over__the country to challenge themselves on the steep roads of Highland County.

The argument

__over__the quality of Fitzgerald ’ s translation of the Rubaiyat has, according to Dougan, diverted attention from**a**fuller understanding of the deeply esoteric message contained in Omar ’ s actual material – "__Every__line of the Rubaiyat has more meaning than almost anything you could read in Sufi literature ".

Every and field

__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__time an MTA receives an email message, it adds

**a**< tt > Received </ tt > trace header

__field__to the top of the header of the message, thereby building

**a**sequential record of MTAs handling the message.

__Every__ordered

__field__

**is**

**a**formally real

__field__, i. e., 0 cannot be written as

**a**sum of nonzero squares.

__Every__instruction consists of

**a**9-bit opcode,

**a**4-bit register code, and

**a**23-bit effective address

__field__, which consists in turn of

**a**1-bit indirect bit,

**a**4-bit register code, and an 18-bit offset.

__Every__

__field__theory of particle physics

**is**based on certain symmetries of nature whose existence

**is**deduced from observations.

__Every__planetary body

**(**including the Earth )

**is**surrounded by its own gravitational

__field__, which exerts an attractive force on all objects.

__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__year, the British Political Studies Association awards the Walter Bagehot Prize for the best dissertation in the

__field__of government and public administration.

__Every__polynomial in can be factorized into polynomials that are irreducible

**over**F. This factorization

**is**unique up to permutation of the factors and the multiplication of the factors by nonzero constants from F

**(**because the ring of polynomials

**over**

**a**

__field__

**is**

**a**unique factorization domain whose units are the nonzero constant polynomials

**).**

__Every__quadratic form q in n variables

**over**

**a**

__field__of characteristic not equal to 2

**is**equivalent to

**a**diagonal form

__Every__kind of material has unique magnetic properties,

**even**those that we do not think of as being “ magnetic .” Different materials below the ground can cause local disturbances in the Earth ’ s magnetic

__field__that are detectable with sensitive magnetometers.

1.100 seconds.