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Some Related Sentences
Every and R
* Every polynomial ring
R ..., x < sub > n </ sub >
is a commutative R-algebra
.
Every holomorphic function can be separated into its real
and imaginary parts,
and each of these
is a solution of Laplace's equation on
R < sup > 2 </ sup >.
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 binary relation
R on
a set S can be extended to
a preorder on S by taking
the transitive closure
and reflexive closure,
R < sup >+=</ sup >.
* 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 separable metric space
is isometric to
a subset of C (),
the separable Banach space of continuous functions →
R, with
the supremum norm
.
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
.
Every random vector gives rise to
a probability measure on
R < sup > n </ sup > with
the Borel algebra as
the underlying sigma-algebra
.
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 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 non-empty set of left ideals of
R, partially ordered by inclusion,
has a maximal element with respect to set inclusion
.
Every year since 1982,
the W
. C
. Handy Music Festival
is held
in the Florence / Sheffield / Muscle Shoals area, featuring blues, jazz, country, gospel, rock music
and R & B
.
Every adult citizen of this small settlement signed
the small petition ; E
. K Dyer
and his wife, William Johnson, Joseph Otis
and his wife, Hiram Walker
and his wife, Joseph Pease
and R. H
. Valentine
.
Every smooth submanifold of
R < sup > n </ sup >
has an induced Riemannian metric g:
the inner product on each tangent space
is the restriction of
the inner product on
R < sup > n </ sup >.
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 single problem touched on thus far
is related to good marketing planning
.
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 man
in every one of these houses
is a Night Rider
.
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 infinite game
in which
is a Borel subset of Baire space
is determined
.
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 root of
a polynomial equation whose coefficients are algebraic numbers
is again algebraic
.
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 M
Every song they wrote was written with an eye toward giving it " deep hidden meaning " or D
. H
. M.
Every smooth
( or differentiable
) map φ:
M → N between smooth
( or differentiable
) manifolds induces natural linear maps between
the corresponding tangent spaces:
Every measurable cardinal κ
is a 0-huge cardinal because < sup > κ </ sup >
M ⊂
M, that
is, every function from κ to
M is in M. Consequently, V < sub > κ + 1 </ sub >⊂
M.

# " 5
. 06 A
. M. ( Every Strangers ' Eyes )"

:
Every countable theory which
is satisfiable
in a model
M,
is satisfiable
in a countable substructure of
M.
* Siegal,
M., Cornell Feline Health Center
( Editors
) ( 1989
) The Cornell Book of Cats: A Comprehensive Medical Reference for
Every Cat
and Kitten
.
* Every endomorphism of
M is either nilpotent or invertible
.
Every year about 5000 applications are received, out of which about 300 students
( around 150
in each year
) are enrolled
in the 2 year full time
M. Tech
.
Every hyperkähler manifold
M has a 2-sphere of complex structures
( i
. e
. integrable almost complex structures
) with respect to which
the metric
is Kähler
.
* Every module
M has an injective hull
.
Every finite-length module
M has a composition series,
and the length of every such composition series
is equal to
the length of
M.
Every year
the department admits students for it
M. A / MSc.,
M. Phil
and Ph
. D courses
.
* Every direct summand of
M is pure
in M. Consequently, every subspace of
a vector space over
a field
is pure
.
0.360 seconds.