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Some Related Sentences
Every and simple
Every finite
simple group
is isomorphic to one
of the following groups:

#
Every simple path from
a given node
to any of its descendant leaves contains
the same number
of black nodes
.
Every simple module is indecomposable
, but
the converse
is in general not true
.
Every simple module is cyclic
, that
is it
is generated by one element
.

" I might easily have written this story in
the traditional manner [...]
Every novelist knows
the recipe [...] It
is not very difficult
to follow
a simple, chronological scheme which
the critics will understand [...] But I
, after all
, am trying
to tell
the story
of this Chapelizod family in
a new way
.
Every October
, Moriarty plays host
to the Pinto Bean Fiesta
, which
is composed
of a bunch
of simple games in Crossly Park
, as well as
a parade and crowning
of a " Pinto Bean Queen
.
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 >.
Every hour that Napoleon could have attacked earlier as he did
, would have been
is his favour
, but
the French could not attack in
the morning for
the simple reason that
the entire army had not yet taken its battle positions
.
Every maximal outerplanar graph
is the visibility graph
of a simple polygon
.
Every closed curve c on X
is homologous
to for some
simple closed curves c < sub > i </ sub >, that
is,

*
Every finite-dimensional
simple algebra over
R must be
a matrix ring over
R, C
, or H
. Every central
simple algebra over
R must be
a matrix ring over
R or H
. These results follow from
the Frobenius theorem
.

*
Every finite-dimensional
simple algebra over C must be
a matrix ring over C and hence every central
simple algebra over C must be
a matrix ring over C
.

*
Every finite-dimensional central
simple algebra over
a finite field must be
a matrix ring over that field
.

*
Every automorphism
of a central
simple algebra
is an inner automorphism ( follows from Skolem – Noether theorem ).

*
Every 4-dimensional central
simple algebra over
a field F
is isomorphic to a quaternion algebra ; in fact
, it
is either
a two-by-two matrix algebra
, or
a division algebra
.
Every simple ring
R with unity
is both left and
right primitive
.

# Personal
right:
Every person has
a right to life but this
right is restricted and has attached certain duties –
simple living
is essential
.
Every Sámi settlement had its seita
, which had no regular shape
, and might consist
of smooth or odd-looking stones picked out
of a stream
, of a small pile
of stones
, of a tree-stump
, or
of a simple post
.

* Rule 2 Each column has
a simple generic model:
Every column can have its own meta-model
Every and R-module
Every finitely-generated
R-module is a direct sum
of these
.

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 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 rectangle
R is in M
. If
the rectangle has length h and breadth k then
a (
R ) =
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 isomorphic

*
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 ordered field contains an ordered subfield that
is isomorphic to the rational numbers
.
Every well-ordered set
is uniquely order
isomorphic to a unique ordinal number
, called
the order type
of the well-ordered set
.

:"
Every group
is naturally
isomorphic to its opposite group "
Every finite-dimensional vector space
is isomorphic to its dual space
, but this isomorphism relies on an arbitrary choice
of isomorphism ( for example
, via choosing
a basis and then taking
the isomorphism sending this basis
to the corresponding dual basis ).
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 universal cover p: D → X
is regular
, with deck transformation group being
isomorphic to the fundamental group
.
Every Riemann surface
is the quotient of a free
, proper and holomorphic action
of a discrete group on its universal covering and this universal covering
is holomorphically
isomorphic ( one also says: " conformally equivalent ")
to one
of the following:

Iwasawa worked with so-called-extensions: infinite extensions
of a number field with Galois group
isomorphic to the additive group
of p-adic integers for some prime p
. Every closed subgroup
of is of the form
, so by Galois theory
, a-extension
is the same thing as
a tower
of fields such that
.

We call
a field E
a splitting field for A if A ⊗ E
is isomorphic to a matrix ring over E
. Every finite dimensional CSA has
a splitting field: indeed
, in
the case when A
is a division algebra
, then
a maximal subfield
of A
is a splitting field
.
Every compact Lie group G
of dimension > 0 has
a subgroup
isomorphic to the circle group
.

(
Every Calabi – Yau manifold in 4 ( real ) dimensions
is a hyperkähler manifold
, because SU ( 2 )
is isomorphic to Sp ( 1 ).

Also
, a kind
of converse holds:
Every algebraic lattice
is isomorphic to Sub ( A ) for some algebra A
.

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 ( 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 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
.

*( Isomorphism-dense )
Every C-object
is isomorphic to some D-object
.

In mathematics
, a quaternion algebra over
a field F
is a central
simple algebra A over F that has dimension 4 over F
. Every quaternion algebra becomes
the matrix algebra by extending scalars (= tensoring with
a field extension ), i
. e
. for
a suitable field extension K
of F
, is isomorphic to the 2 × 2 matrix algebra over K
.
0.276 seconds.