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Page "Primitive ring" ¶ 9
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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 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 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.
# 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 ring
** Every unital ring other than the trivial ring contains a maximal ideal.
* Every polynomial ring R ..., x < sub > n </ sub > is a commutative R-algebra.
Every Boolean algebra ( A, ∧, ∨) gives rise to a ring ( A, +, ·) by defining a + b := ( a ∧ ¬ b ) ∨ ( b ∧ ¬ a ) = ( a ∨ b ) ∧ ¬( a ∧ b ) ( this operation is called symmetric difference in the case of sets and XOR in the case of logic ) and a · b := a ∧ b. The zero element of this ring coincides with the 0 of the Boolean algebra ; the multiplicative identity element of the ring is the 1 of the Boolean algebra.
In Norse mythology, Draupnir ( Old Norse " the dripper ") is a gold ring possessed by the god Odin with the ability to multiply itself: Every ninth night eight new rings ' drip ' from Draupnir, each one of the same size and weight as the original.
Every module over a division ring has a basis ; linear maps between finite-dimensional modules over a division ring can be described by matrices, and the Gaussian elimination algorithm remains applicable.
Every division ring is therefore a division algebra over its center.
Every objective has a different size ring, so for every objective another condenser setting has to be chosen.
Every match must be assigned a rule keeper known as a referee, who is the final arbitrator ( In multi-man lucha libre matches, two referees are used, one inside the ring and one outside ).
* 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.
* Krull's theorem ( 1929 ): Every ring with a multiplicative identity has a maximal ideal.
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 finitely-generated commutative algebra over a commutative Noetherian ring is Noetherian.
* Every localization of a commutative Noetherian ring is Noetherian.
Every topological ring is a topological group ( with respect to addition ) and hence a uniform space in a natural manner.
Every prostaglandin contains 20 carbon atoms, including a 5-carbon ring.
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 and R
* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =
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 >.
* Every separable metric space is isometric to a subset of C (), the separable Banach space of continuous functions → R, with the supremum norm.
Every random vector gives rise to a probability measure on R < sup > n </ sup > with the Borel algebra as the underlying sigma-algebra.
* 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 >.

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