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 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 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 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.