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Some Related Sentences
Every and Boolean
Every Boolean ring R satisfies x ⊕ x
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 finitely generated ideal
of a Boolean ring is principal
( indeed
, ( x
, y )=( x
+ y
+ xy )).
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 Boolean algebra is a Heyting
algebra, with given
by.

*
Every Boolean algebra is a distributive lattice
.

:
Every Boolean algebra contains
a prime ideal
.
Every complemented distributive lattice has
a unique orthocomplementation
and is in fact
a Boolean algebra.
Every Boolean algebra can be represented as
a field
of sets.
Every finite
Boolean algebra can be represented as
a whole power set-the power set
of its set
of atoms
; each
element of the Boolean algebra corresponds
to the set
of atoms below it
( the join
of which
is the element ).
Every ( normal
) Boolean algebra with operators can be represented as
a field
of sets on
a relational structure
in the sense that it
is isomorphic
to the complex
algebra corresponding
to the field
.
Every Boolean algebra A has an essentially unique completion
, which
is a complete
Boolean algebra containing
A such that every
element is the supremum
of some subset
of A.

*
Every finite
Boolean algebra is complete
.

*
Every subset
of a complete
Boolean algebra has
a supremum
, by definition
; it follows that every subset also has an infimum
( greatest lower bound ).
Every and algebra
Every associative
algebra is obviously alternative
, but so too are some strictly nonassociative algebras such as
the octonions
.

*
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 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 division
ring is therefore
a division
algebra over its center
.
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 finitely-generated commutative
algebra over
a commutative Noetherian
ring is Noetherian
.
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 state on
a C *-
algebra is of the above type
.
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 gives
Every LORAN chain
in the world uses
a unique Group Repetition Interval
, the number
of which
, when multiplied
by ten
, gives how many microseconds pass between pulses from
a given station
in the chain
.
Every year
, the International Documentary Festival
in Amsterdam
( IDFA
) gives an acclaimed filmmaker
the chance
to screen his or her personal Top 10 favorite films
.

*
Every finite topological space
gives rise to a preorder on its points
, in which x ≤ y if
and only if x belongs
to every neighborhood
of y
, and every finite preorder can be formed as
the specialization preorder
of a topological space
in this way
.
Every thing depends upon
the evil
of the second order
; it
is this which
gives to such actions
the character
of crime
, and which makes punishment necessary
.
Every adjunction 〈 F
, G
, ε
, η 〉
gives rise to an associated monad 〈 T
, η
, μ 〉
in the category D
. The functor
Every ticket
is provided
with a bar code that
gives information about
the time
the visitor stepped into
the museum
.
Every coalgebra
, by ( vector space
) duality
, gives rise to an
algebra, but not
in general
the other way
.
Every broadcasting company has members
and the number
of members
gives them
a status that
is connected
to the number
of hours
of broadcasting
.
The WBC launched
a website
called Priests Rape Boys
in which they criticize
the Roman Catholic Church because
of the Catholic sex abuse scandal
, saying
, "
Every time any person
gives any amount
of money
to the Catholic Church
, that person
is paying
the salary
of pedophile rapists
.
Every year
, the magazine
gives out its Utne Independent Press Awards
, which honor alternative
and independent magazines from around
the world
.

This flat may be identified
with the partition
of the vertices
of into
the connected components
of the subgraph formed
by:
Every set
of edges having
the same closure as
gives rise to the same partition
of the vertices
, and may be recovered from
the partition
of the vertices
, as it consists
of the edges whose endpoints both belong
to the same set
in the partition
.
Every sequence
of A, B
, and C without immediate repetition
of the same one
is possible
and gives an equally dense packing for spheres
of a given radius
.
Every year
the American Society
of Architectural Illustrators
gives out
the Hugh Ferriss Memorial Prize for architectural rendering excellence
.
Every door
, whether it leads
to nothing or
a level boss
, gives the player
a question mark ('?
Every hearts gotten
gives the player-5 points
.
Every trick taken
gives a player 10 points
.
Every group
gives a quandle where
the operations come from conjugation:
Every year
, the IDFA
, International Documentary Festival
in Amsterdam
, gives an acclaimed filmmaker
the chance
to screen his or her personal Top 10 favorite films
.
Every year
, she
gives a speech
to cadets from throughout Civil Air Patrol at
the National Honor Guard Academy
and also
to a gathered assembly
of basic cadets
and staff at
the Civil Air Patrol's Tri-Wing Encampment
, held
by Maryland Wing
.
Every episode
gives credits
to James Burrows
, Glen Charles
and Les Charles
, the creators
of Cheers
, the show where
the character
of Dr
. Frasier Crane originated
.
Every evening
, she
gives another twelve-minute address
.
Every year
the Museum
gives "
The Wrangler ", an original bronze sculpture
by artist John Free
.
Every year
, Gourmand
gives the awards
in a very special location for gastronomy
.
0.390 seconds.