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* Every reduced commutative k-algebra A is a separable algebra ; i. e., is reduced for every field extension F / k.

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## Some Related Sentences

Every and reduced

__Every__10 percent increase in the price of cigarettes

__reduced__youth smoking by about seven percent and overall cigarette consumption by about four percent

**.**

__Every__five years the NZ Transport Agency will embark on

**a**state highway review to consider whether the existing network should be expanded or

__reduced__, according to traffic flows, changes in industry, tourism and development

**.**

*****

__Every__first time purchaser of an automobile deprived the streetcars operator of income whilst simultaneously created additional traffic congestion which often

__reduced__service speeds and thereby increased their operational costs and making the services less attractive to the remaining users

**.**

__Every__

**field**officer of his brigade was killed or wounded save two, and his brigade, already sadly

__reduced__by its terrible sacrifices at Chancellorsville, lost in nearly 550 men out of the 1, 350 engaged

**.**

__Every__

**field**and

**every**polynomial ring over

**a**

**field**( in arbitrarily many variables )

**is**

**a**

__reduced__ring

**.**

__Every__other interchange with major roads along the route ( Toorak, Burke, Tooronga and Warrigal Roads ) was an at-grade intersection controlled by traffic-lights, and because the road was constructed through residential areas,

__reduced__speed limits were also enforced

**.**

*****

__Every__time

**a**loan balance

**is**

__reduced__, an equivalent number of bonds are identified by lottery and converted into

**a**different bond also with

**a**one cent par value ( that will convert at par into cash at the next payment date ).

__Every__new Queen's Counsel created

__reduced__the Serjeants in importance, since even the most junior QC took precedence over the most senior Serjeant

**.**

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__

__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 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

**.**

Every and separable

*****

__Every__

__separable__metric space

**is**isometric to

**a**subset of the ( non-separable ) Banach space l < sup >∞</ sup > of all bounded real sequences with the supremum norm

**;**this

**is**known as the Fréchet embedding

**.**

*****

__Every__

__separable__metric space

**is**isometric to

**a**subset of C (), the

__separable__Banach space of continuous functions → R, with the supremum norm

**.**

__Every__metric space which

**is**ccc

**is**also

__separable__, but in general

**a**ccc topological space need not be

__separable__

**.**

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