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* Every localization of a commutative Noetherian ring is Noetherian.

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## Some Related Sentences

Every and localization

:"

__Every__one who has been fortunate enough to hear the telephones at the Palais de l ' Industrie has remarked that, in listening with both ears at the two telephones, the sound takes**a**special character**of**relief and__localization__which**a**single receiver cannot produce ...

Every and commutative

*****

__Every__

__commutative__real unital

**Noetherian**Banach algebra with no zero divisors

**is**isomorphic to the real or complex numbers

**.**

*****

__Every__

__commutative__real unital

**Noetherian**Banach algebra ( possibly having zero divisors )

**is**finite-dimensional

**.**

*****

__Every__reduced

__commutative__k-algebra A

**is**

**a**separable algebra ; i

**.**e.,

**is**reduced for every field extension F / k

**.**

__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

**.**

Every and Noetherian

__Every__semisimple

**ring**

**is**von Neumann regular, and

**a**left ( or right )

__Noetherian__von Neumann regular

**ring**

**is**semisimple

**.**

Every and ring

__Every__Boolean algebra ( A, ∧, ∨) gives rise to

**a**

__ring__( A, +, ·) by defining

**a**+ b := (

**a**∧ ¬ b ) ∨ ( b ∧ ¬

**a**) = (

**a**∨ b ) ∧ ¬(

**a**∧ b ) ( this operation

**is**called symmetric difference in the case

**of**sets and XOR in the case

**of**logic ) and

**a**· b :=

**a**∧ b

**.**The zero element

**of**this

__ring__coincides with the 0

**of**the Boolean algebra ; the multiplicative identity element

**of**the

__ring__

**is**the 1

**of**the Boolean algebra

**.**

In Norse mythology, Draupnir ( Old Norse " the dripper ")

**is****a**gold__ring__possessed by the god Odin with the ability to multiply itself:__Every__ninth night eight new rings ' drip ' from Draupnir, each one**of**the same size and weight as the original**.**__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__objective has

**a**different size

__ring__, so for every objective another condenser setting has to be chosen

**.**

__Every__match must be assigned

**a**rule keeper known as

**a**referee, who

**is**the final arbitrator ( In multi-man lucha libre matches, two referees are used, one inside the

__ring__and one outside ).

*****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__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__topological

__ring__

**is**

**a**topological group ( with respect to addition ) and hence

**a**uniform space in

**a**natural manner

**.**

__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 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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