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* Every finitely-generated commutative algebra over a commutative Noetherian ring is Noetherian.

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## Some Related Sentences

Every and finitely-generated

A

__finitely-generated__abelian group**is**indecomposable if and only if it**is**isomorphic to Z or to**a**factor group of the form for some prime number p and some positive integer n**.**__Every____finitely-generated__abelian group**is****a**direct sum of ( finitely many ) indecomposable abelian groups**.**

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 algebra

__Every__associative

__algebra__

**is**obviously alternative, but so too are some strictly nonassociative algebras such as the octonions

**.**

__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__

**.**

*****

__Every__real Banach

__algebra__which

**is**

**a**division

__algebra__

**is**isomorphic to the reals, the complexes, or the quaternions

**.**

*****

__Every__unital real Banach

__algebra__with no zero divisors, and in which every principal ideal

**is**closed,

**is**isomorphic to the reals, the complexes, or the quaternions

**.**

__Every__continuous map f: X → Y induces an

__algebra__homomorphism C ( f ): C ( Y ) → C ( X ) by the rule C ( f )( φ ) = φ o f for every φ in C ( Y ).

__Every__vector v in determines

**a**linear map from R to taking 1 to v, which can be thought of as

**a**Lie

__algebra__homomorphism

**.**

__Every__associative

__algebra__

**is**obviously power-associative, but so are all other alternative algebras ( like the octonions, which are non-associative ) and even some non-alternative algebras like the sedenions

**.**

__Every__random vector gives rise to

**a**probability measure on R < sup > n </ sup > with the Borel

__algebra__as the underlying sigma-algebra

**.**

__Every__finite-dimensional Hausdorff topological vector space

**is**reflexive, because J

**is**bijective by linear

__algebra__, and because there

**is**

**a**unique Hausdorff vector space topology on

**a**finite dimensional vector space

**.**

__Every__Boolean

__algebra__can be obtained in this way from

**a**suitable topological space: see Stone's representation theorem for Boolean algebras

**.**

__Every__Boolean

__algebra__

**is**

**a**Heyting

__algebra__when

**a**→ b

**is**defined as usual as ¬

**a**∨ b, as

**is**every complete distributive lattice when

**a**→ b

**is**taken to be the supremum of the set of all c for which

**a**∧ c ≤ b

**.**The open sets of

**a**topological space form

**a**complete distributive lattice and hence

**a**Heyting

__algebra__

**.**

__Every__Heyting

__algebra__with exactly one coatom

**is**subdirectly irreducible, whence every Heyting

__algebra__can be made an SI by adjoining

**a**new top

**.**

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__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__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 ".0.254 seconds.