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Some Related Sentences
Every and field

**
Every field has an algebraic closure.

**
Every field extension has a transcendence basis
.
Every field is,
of course, one-dimensional over
its center
.
Every time
an MTA receives
an email message, it adds a < tt > Received </ tt > trace header
field to
the top
of the header
of the message, thereby building a sequential record
of MTAs handling
the message
.
Every subfield
of an ordered
field is also
an ordered
field in the inherited order
.
Every ordered
field contains
an ordered subfield that
is isomorphic to
the rational numbers
.
Every ordered
field is a formally real
field.
Every subfield
of an ordered
field is also
an ordered
field ( inheriting
the induced ordering ).
Every ordered
field can be embedded into
the surreal numbers
.
Every ordered
field is a formally real
field, i
. e., 0 cannot be written as a sum
of nonzero squares
.
Every instruction consists
of a 9-bit opcode, a 4-bit register code, and a 23-bit effective address
field,
which consists
in turn
of a 1-bit indirect bit, a 4-bit register code, and
an 18-bit offset
.
Every field theory
of particle physics
is based on certain symmetries
of nature whose existence
is deduced from observations
.
Every planetary body
( including
the Earth )
is surrounded by
its own gravitational
field,
which exerts
an attractive force on all objects
.
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 local
field is isomorphic
( as a topological
field ) to one
of the following:
Every year,
the British Political Studies Association awards
the Walter Bagehot Prize for
the best dissertation
in the field of government and public administration
.
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 quadratic
form q
in n variables over a
field of characteristic not equal to 2
is equivalent to a diagonal
form
Every kind
of material
has unique magnetic properties, even those that we do not think
of as being “ magnetic .” Different materials below
the ground can cause local disturbances
in the Earth ’ s magnetic
field that are detectable with sensitive magnetometers
.
Every and has
Every soldier
in the army
has, somewhere, relatives who are close to starvation
.
Every woman
has had
the experience
of saying no when she meant yes, and saying yes when she meant no
.
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 calculation
has been made independently by two workers and checked by one
of the editors
.
Every retiring person
has a different situation facing him
.
Every family
of Riviera Presbyterian Church
has been asked to read
the Bible and pray together daily during National Christian Family Week and to undertake one project
in which all members
of the family participate
.
Every community, if it
is alive
has a spirit, and that spirit
is the center
of its unity and identity
.

``
Every woman
in the block
has tried that ''
.

:
Every set
has a
choice function
.
Every such subset
has a smallest element, so to specify our
choice function we can simply say that it maps each set to
the least element
of that set
.

**
Every surjective function
has a right inverse
.

** Zorn's lemma:
Every non-empty partially ordered set
in which every chain
( i
. e
. totally ordered subset )
has an upper bound contains at least one maximal element
.

The restricted principle "
Every partially ordered set
has a maximal totally ordered subset "
is also equivalent to AC over ZF
.

** Tukey's lemma:
Every non-empty collection
of finite character
has a maximal element with respect to inclusion
.

** Antichain principle:
Every partially ordered set
has a maximal antichain
.

**
Every vector space
has a basis
.

*
Every small category
has a skeleton
.

*
Every continuous functor on a small-complete category
which satisfies
the appropriate solution set condition
has a left-adjoint
( the Freyd adjoint functor theorem ).

**
Every Tychonoff space
has a Stone – Čech compactification
.

*
Every rectangle R
is in M
. If
the rectangle
has length h and breadth k then a
( R ) =
Every unit
of length
has a corresponding unit
of area, namely
the area
of a square with
the given side length
.
Every ATM cell
has an 8-or 12-bit Virtual Path Identifier
( VPI ) and 16-bit Virtual Channel Identifier
( VCI ) pair defined
in its header
.
0.111 seconds.