[permalink] [id link]

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.

from
Wikipedia

## Some Related Sentences

We and call

__We__should spread

**the**view that planning and national development are serious matters which

__call__

**for**effort as well as enthusiasm

**.**

__We__have only

**to**think

**of**Lady Macbeth or

**the**policeman-murderer

**in**Thomas Burke's famous story

**,**`` The Hands Of Mr. Ottermole ''

**,**

**to**realize that hands often

__call__up ideas

**of**crime and punishment

**.**

Why

**,**man**,**that's**the**same kind**of**music we've been playin ' since 1928 !...__We__didn't__call__it rock and roll back**when**we introduced it as our style back**in**1928**,**and we don't__call__it rock and roll**the**way we play it now**.**
Attlee responded

**the**next day**in****the**debate on increased air estimates that Hitler's speech contained unfavourable references**to****the**Soviet Union but that "__We__see here**a**chance**to**__call__**a**halt**in****the**armaments race ...__We__do not think that our answer**to**Herr Hitler should be just rearmament**.**__We__will

__call__

**the**first

**the**furnace and

**the**second

**the**refrigerator .” Carnot

**then**explains how we can obtain motive power

**,**i

**.**e

**.**“ work ”, by carrying

**a**certain quantity

**of**heat from body

**A**

**to**body B

**.**

In 1945

**,**Engelbart had read with interest Vannevar Bush's article " As__We__May Think ",**a**__call__**to**action**for**making knowledge widely available as**a**national peacetime grand challenge**.**
* "

__We__shot music**,**__call__it murder on**the**dancefloor**,**and we got more bars than wandsworth and dartmoor "-Dartmoor Prison**,**mentioned**in**Devlin's song Shot Music ( May 10**,**2010 )
Let us

__call__**the**class**of**all such formulas R**.**__We__are faced with proving that every formula**in**R**is**either refutable or satisfiable**.**
:"

__We__worship ," replied Hengist**,**" our country gods**,**Saturn and Jupiter**,**and**the**other deities that govern**the**world**,**but especially Mercury**,**whom**in**our language we__call__Woden and**to**whom our ancestors consecrated**the**fourth day**of****the**week**,**still called after his name Wodensday**.**
Savoy dancer " Shorty " George Snowden stated that "

__We__used**to**__call__**the**basic step**the**Hop long before Lindbergh did his hop across**the**Atlantic**.**__We__may represent any given proposition with

**a**letter which we

__call__

**a**propositional constant

**,**analogous

**to**representing

**a**number by

**a**letter

**in**mathematics

**,**

**for**instance

**,**

**.**

__We__understand that shows don't want

**to**

__call__

**the**writers writers because they want

**to**maintain

**the**illusion that it

**is**reality

**,**that stuff just happens

**.**

We and field

__We__do not favor one

__field__

**over**another

**:**we think that all inquiry

**,**all scholarly and artistic creation

**,**

**is**good -- provided only that it contributes

**to**

**a**sense and understanding

**of**

**the**true ends

**of**life

**,**as all first-rate scholarship and artistic creation does

**.**

__We__can do this through

**the**characteristic values and vectors

**of**T

**in**certain special cases

**,**i.e.

**,**

**when**

**the**minimal polynomial

**for**T factors

**over**

**the**scalar

__field__F into

**a**product

**of**distinct monic polynomials

**of**degree 1

**.**

__We__might not see any rotation initially

**,**but

**if**we closely look at

**the**right

**,**we see

**a**larger

__field__at

**,**say

**,**x = 4 than at x = 3

**.**

__We__have evidence that Jupiter

**has**

**a**magnetic

__field__and that birds are oviparous

**,**but as

**of**yet

**,**we do not seem

**to**have found evidence

**of**moral properties

**,**such as " goodness ".

__We__have previously mentioned that there can be more than one way

**of**indexing

**the**degrees

**of**freedom

**in**

**a**quantum

__field__

**.**

)

__We__can construct__field__operators by applying**the**Fourier transform**to****the**creation and annihilation operators**for**these states**.**__We__take

**the**velocity

__field__associated with this current as

**the**velocity

__field__whose integral curves yield

**the**motion

**of**

**the**particle

**.**

__We__conclude that

**,**

**in**

**the**

__field__

**of**public education

**,**

**the**doctrine

**of**" separate but equal "

**has**no place

**.**

__We__provide

**a**sketch

**of**

**a**proof

**for**

**the**

**case**where

**the**underlying

__field__

**of**scalars

**is**

**the**complex numbers

**.**

__We__have

**,**therefore

**,**directed

**the**Irish Army authorities

**to**have

__field__hospitals established

**in**County Donegal adjacent

**to**Derry and at other points along

**the**Border where they may be necessary

**.**

(

__We__developed )**a**theory**to**explain how solar protons can diffuse inward and gain energy**in****the**Earth's magnetic__field__**.**__We__now recognise this as part

**of**

**the**ideal class group

**:**

**in**fact Kummer had isolated

**the**p-torsion

**in**that group

**for**

**the**

__field__

**of**p-roots

**of**unity

**,**

**for**any prime number p

**,**as

**the**reason

**for**

**the**failure

**of**

**the**standard method

**of**attack on

**the**Fermat problem ( see regular prime ).

__We__can assume that

**A**contains ¬ φ

**,**

**the**

__field__axioms

**,**and

**,**

**for**some k

**,**

**the**first k sentences

**of**

**the**form 1 + 1 +...+ 1 ≠ 0 ( because adding more sentences doesn't change unsatisfiability ).

__We__can construct

**a**classical continuous random

__field__that

**has**

**the**same probability density as

**the**quantum vacuum state

**,**so that

**the**principal difference from quantum

__field__theory

**is**

**the**measurement theory ( measurement

**in**quantum theory

**is**different from measurement

**for**

**a**classical continuous random

__field__

**,**

**in**that classical measurements are always mutually compatible —

**in**quantum mechanical terms they always commute ).

__We__assume that

**the**underlying

__field__

**is**not

**of**characteristic 2

**:**that

**is**

**,**that where 1 denotes

**the**multiplicative identity and 0

**the**additive identity

**of**

**the**given

__field__

**.**

__We__claim that

**,**as

**a**

__field__

**,**

**the**quotient

**is**

**isomorphic**

**to**

**the**complex numbers

**,**C

**.**

**A**general complex number

**is**

**of**

**the**form

**,**where

**a**and b are real numbers and Addition and multiplication are given by

0.249 seconds.