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Any quotient of a ring by a maximal ideal is a simple ring.

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## Some Related Sentences

Any and quotient

__Any__normal subgroup has

**a**corresponding

__quotient__group, formed from the larger group

**by**eliminating the distinction between elements

**of**the subgroup

**.**

__Any__such surface

**is**the Kummer variety

**of**the Jacobian

**of**

**a**smooth hyperelliptic curve

**of**genus 2 ; i

**.**e

**.**

**a**

__quotient__

**of**the Jacobian

**by**the Kummer involution x ↦ − x

**.**

*

__Any__irreducible representation R**of**H gives an irreducible representation**of**G using the__quotient__map from G to H ( that**is**, as**a**restricted representation ).

Any and ring

*

__Any____ring__**of**matrices with coefficients in**a**commutative__ring__R forms an R-algebra under matrix addition and multiplication**.**__Any__legal wrestler

**is**open to attack from any direction at any time, including when they are downed, as long as they are within the

__ring__area enclosed

**by**the

__ring__ropes

**.**

__Any__number system that forms

**a**commutative

__ring__— for instance, the integers, the real numbers, and the complex numbers — can be extended to

**a**wheel in which division

**by**zero

**is**always possible ; however, in such

**a**case, " division " has

**a**slightly different meaning

**.**

*

__Any____ring__R can be considered as**a**one-object preadditive category ; the category**of**left modules over R**is**the same as the additive functor category Add ( R, Ab ) ( where Ab denotes the category**of**abelian groups ), and the category**of**right R-modules**is**Add ( R < sup > op </ sup >, Ab ).__Any__prime number p gives rise to an

**ideal**pO < sub > K </ sub > in the

__ring__

**of**integers O < sub > K </ sub >

**of**

**a**quadratic field K

**.**

*

__Any__algebra over**a**commutative__ring__K may be regarded as**a**purely even superalgebra over K ; that**is**,**by**taking A < sub > 1 </ sub > to be trivial**.**__Any__n-dimensional formal group law gives an n dimensional Lie algebra over the

__ring__R, defined in terms

**of**the quadratic part F < sub > 2 </ sub >

**of**the formal group law

**.**

Any and by

__Any__fee so determined shall be entered as

**a**part

**of**such award, and payment thereof shall be made

__by__the Secretary

**of**the Treasury

__by__deducting the amount thereof from the total amount paid pursuant to the award

**.**

__Any__and all payments required to be made

__by__the Secretary

**of**the Treasury under this title pursuant to any award made

__by__the Commission to the Government

**of**the United States shall be covered into the Treasury to the credit

**of**miscellaneous receipts

**.**

__Any__irregularity on the piston heads will make it impossible, with normal means, to determine the final combustion chamber volume because the volume displaced

__by__the piston heads cannot be readily computed

**.**

__Any__free elections that were to be held in Poland would have to produce

**a**government in which Moscow had complete confidence, and all pressure from the West for free voting

__by__anti-Soviet elements in Poland would be met

__by__restrictions on voting

__by__these elements

**.**

__Any__example

**of**grand or exquisite diction may have been created

__by__the poet who compiled numerous lays into the two works we possess or may be due to one

**of**his completely unknown fellow-craftsmen

**.**

__Any__animal could when travelin' fast, be sent heels over head

__by__the

**simple**process

**of**overtakin' the brute, seizin' its tail, and givin' the latter

**a**pull to one side

**.**

__Any__needy family living in San Francisco can obtain toys

__by__writing to Christmas Toys, 676 Howard street, San Francisco 5, and listing the parent's name and address and the age and sex

**of**each child in the family between the ages

**of**1 and 12

**.**

__Any__information may be conveyed

__by__an analog signal ; often such

**a**signal

**is**

**a**measured response to changes in physical phenomena, such as sound, light, temperature, position, or pressure

**.**

__Any__quantity

**of**energy absorbed

__by__the electron in excess

**of**this amount

**is**converted to kinetic energy according to the conservation

**of**energy

**.**

__Any__individual has one

**of**six possible genotypes ( AA, AO, BB, BO, AB, and OO ) that produce one

**of**four possible phenotypes: " A " ( produced

__by__AA homozygous and AO heterozygous genotypes ), " B " ( produced

__by__BB homozygous and BO heterozygous genotypes ), " AB " heterozygotes, and " O " homozygotes

**.**

__Any__individual alignment could indicate

**a**direction

__by__chance, but he planned to show that together the distribution

**of**alignments was non-random, showing that there was an astronomical intent to the orientation

**of**at least some

**of**the alignments

**.**

__Any__node in the data structure can be reached

__by__starting at root node and repeatedly following references to either the left or right child

**.**

__Any__other craters that might have formed in the Tethys Ocean would have been obscured

__by__tectonic events like the relentless northward drift

**of**Africa and India

**.**

__Any__differential area with normal vector

**of**

**a**given internal surface area, bounding

**a**portion

**of**the body, experiences

**a**contact force arising from the contact between both portions

**of**the body on each side

**of**, and it

**is**given

__by__

*

__Any__locally compact Hausdorff space can be turned into**a**compact space__by__adding**a**single point to it,__by__means**of**Alexandroff one-point compactification**.**__Any__season ticket holder could put themselves forward for election, with

**a**certain number

**of**nominations, and votes were cast

__by__all season ticket holders over the age

**of**18

**.**

*

__Any__non-Jewish slave bought__by__**a**Jew will be confiscated__by__the state ; if**a**Jew attempts to circumcise**a**non-Jewish slave, the slave will be freed and the Jew shall face capital punishment ; any Christian slaves owned__by__**a**Jew will be taken away and freed ;0.355 seconds.