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Some Related Sentences
Every and finitely

Hilbert's example: " the assertion that either there are only
finitely many prime numbers or there are infinitely many "
( quoted in Davis 2000: 97 ); and Brouwer's: "
Every mathematical species
is either finite or infinite.

#
Every finitely generated ideal of A
is principal ( i. e., A
is a Bézout domain ) and A satisfies the ascending chain condition on
principal ideals.

*
Every finitely generated group with
a recursively enumerable presentation and insoluble word problem
is a subgroup
of a finitely presented group with insoluble word problem
Every subset
of a nowhere dense set
is nowhere dense
, and the union
of finitely many nowhere dense sets
is nowhere dense.

*
Every left
ideal I in R
is finitely generated, i. e. there exist elements
a < sub > 1 </ sub >, ...,
a < sub > n </ sub > in I such that I = Ra < sub > 1 </ sub >
+ ...
+ Ra < sub > n </ sub >.
Every finitely presented group
is recursively presented
, but there are recursively presented groups that cannot be
finitely presented.
Every one
of the infinitely many vertices
of G can be reached from v < sub > 1 </ sub > with
a simple path
, and each such path must start with one
of the
finitely many vertices adjacent to v < sub > 1 </ sub >.

" I can now state the physical version
of the Church-Turing principle: '
Every finitely realizable physical system can be perfectly simulated by
a universal model computing machine operating by finite means.

*
Every substructure
is the union
of its
finitely generated substructures ; hence Sub
( A )
is an algebraic lattice.

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.

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 ( bounded ) convex polytope
is the image
of a simplex
, as every point
is a convex combination
of the
( finitely many ) vertices.
Every and generated
Every simple module
is cyclic
, that
is it
is generated by one element.
Every group
of prime order
is cyclic
, since Lagrange's theorem implies that the cyclic subgroup
generated by
Every lattice in can be
generated from
a basis for the vector space by forming all linear combinations with integer coefficients.
Every film today
, whether it be live-action
, computer
generated, or traditional hand-drawn animation
is made up
of hundreds
of individual shots that are all placed together during editing to form the single film that
is viewed by the audience.

A large part
of the interest
generated was due to the eclectic mix
of samples and influences
, evident on
Every Man and Woman
, which was dedicated to Dewey Bunnell
of the band America.

*
Every compact space
is compactly
generated.

*
Every locally compact space
is compactly
generated.

*
Every first-countable space
is compactly
generated.

*
Every CW complex
is compactly
generated Hausdorff.
Every ticket
generated by the system has persistence or " history " showing what happened to the ticket within its life cycle.
Every profile also captures some non-crime statistics: the amount
of overtime
generated by members
of the command
, the number
of department vehicle accidents
, absence rates due to sick time and line-of-duty injuries
, and the number
of civilian complaints lodged against members
of the unit.
Every and ideal

**
Every unital
ring other than the trivial
ring contains
a maximal
ideal.

*
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 character
is automatically continuous from A to C
, since the kernel
of a character
is a maximal
ideal, which
is closed.

* 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 principal ideal domain
is a unique factorization domain
( UFD ).

#
Every principal ideal domain
is Noetherian.

#
Every prime
ideal of A
is principal.
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.

* Krull's theorem
( 1929 ):
Every ring with
a multiplicative identity has
a maximal
ideal.
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.
( DD1 )
Every nonzero proper
ideal factors into primes.
( DD3 )
Every fractional
ideal of is invertible.
Every field
of either type can be realized as the field
of fractions
of a Dedekind domain in which every non-zero
ideal is of finite index.

:
Every Boolean algebra contains
a prime
ideal.
Every element
of the Baer radical
is nilpotent
, so it
is a nil
ideal.

In Leedskalnin's own publication A Book in
Every Home he implies his " Sweet Sixteen " was more an
ideal than
a reality.

*
Every localization
of R at
a maximal
ideal is a field
Every meal can be eaten without any cooking ; when circumstances permit
, the
ideal method
of preparation
is to cook the entrees in
a pressure cooker
, heated on the standard issue Coleman stove
, or by simply boiling the rations in its package in water.
Every free spirit looked upon her as protectoress and
ideal .... Marguerite was the embodiment
of charity.
0.541 seconds.