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* Every commutative semisimple ring must be a finite direct product of fields.

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## Some Related Sentences

Every and commutative

*****

__Every__

__commutative__real unital Noetherian Banach algebra with no zero divisors is isomorphic to the real or complex numbers

**.**

*****

__Every__

__commutative__real unital Noetherian Banach algebra ( possibly having zero divisors ) is finite-dimensional

**.**

*****

__Every__reduced

__commutative__k-algebra A is

**a**separable algebra ; i

**.**e., is reduced for every field extension F / k

**.**

__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

**.**

Every and semisimple

__Every__

__semisimple__

**ring**is von Neumann regular, and

**a**left ( or right ) Noetherian von Neumann regular

**ring**is

__semisimple__

**.**

__Every__

**ring**which is

__semisimple__as

**a**module over itself has zero Jacobson radical, but not every

**ring**with zero Jacobson radical is

__semisimple__as

**a**module over itself

**.**

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 must

*****

__Every__collecting institution

__must__develop an emergency plan to protect its collections and train staff to carry it out

**.**

__Every__cleric in Holy Orders and every member

**of**

**a**religious order

__must__publicly join in or privately read aloud ( i

**.**e

**.**using the lips as well as the eyes — it takes about two hours in this way ) the whole

**of**the Breviary services allotted for each day

**.**

__Every__DNS zone

__must__

**be**assigned

**a**set

**of**authoritative name servers that are installed in NS records in the parent zone, and should

**be**installed ( to

**be**authoritative records ) as self-referential NS records on the authoritative name servers

**.**

__Every__system

__must__have

**a**class designated as " root ", with one

**of**its creation procedures designated as " root procedure ".

__Every__SE

__must__

**be**registered in the State where it has its registered office, in

**a**register designated by the law

**of**that State

**.**

In cybernetics, the Good Regulator or Conant-Ashby theorem is stated "

__Every__Good Regulator**of****a**system__must__**be****a**model**of**that system ".*****Tested:

__Every__change

__must__

**be**tested in

**a**safe test environment, which closely reflects the actual production environment, before the change is applied to the production environment

**.**

__Every__U

**.**S

**.**jurisdiction has its own regulations regarding what, precisely,

__must__

**be**said to

**a**person arrested or placed in

**a**custodial situation

**.**

__Every__adult, healthy, sane Muslim who has the financial and physical capacity to travel to Mecca and can make arrangements for the care

**of**his / her dependants during the trip,

__must__perform the Hajj once in

**a**lifetime

**.**

*****

__Every__formal address or message " to the nation " or to either or both Houses

**of**the Oireachtas

__must__have prior approval

**of**the Government

**.**

The moral law stands on an entirely different foundation from the ceremonial or ritual law ....

__Every__part**of**this law__must__remain in force upon all mankind and in all ages**.**
Historian Barry Adam notes, "

__Every__social movement__must__choose at some point what to retain and what to reject out**of**its past**.**
The last two lines

**of**the Act IV-scene 2 funeral song may also have inspired the lines W**.**H**.**Auden, the librettist for Stravinsky's The Rake's Progress, puts into the mouth**of**Anne Truelove at the end**of**the opera: "__Every__wearied body__must__late or soon return to dust ".__Every__time you move to

**a**new page, however, the server

__must__believe that you are the same person who originally signed in ( otherwise it will refuse ).

__Every__twin prime pair except ( 3, 5 ) is

**of**the form ( 6n − 1, 6n + 1 ) for some natural number n, and with the exception

**of**< var > n </ var > = 1, < var > n </ var >

__must__end in 0, 2, 3, 5, 7, or 8

**.**

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