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Every simple ring R with unity is both left and right primitive.

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## Some Related Sentences

Every and simple

#

__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

**.**

" 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__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

**.**

Every and ring

__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__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**.**__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__topological

__ring__

**is**a topological group (

**with**respect to addition )

**and**hence a uniform space in a natural manner

**.**

__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__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 >.

0.252 seconds.