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* Any two-sided ideal of a ring R is an R-bimodule.

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Wikipedia

## Some Related Sentences

Any and ideal

__Any__Banach algebra ( whether it has

**an**identity element or not ) can be embedded isometrically into

**a**unital Banach algebra so as to form

**a**closed

__ideal__

**of**

**.**

*****Norton's theorem:

__Any__network

**of**voltage or current sources and resistors

**is**electrically equivalent to

**an**

__ideal__current source in parallel with

**a**single resistor

**.**

__Any__philosophy that assigns crucial importance to the

__ideal__or spiritual realm in its account

**of**human existence may be termed " idealist ".

*****

__Any__principal

__ideal__domain, such as the integers,

**is**Noetherian since every

__ideal__

**is**generated by

**a**single element

**.**

__Any__black box containing only voltage sources, current sources, and other resistors can be converted to

**a**Norton equivalent circuit, comprising exactly one

__ideal__current source and one resistor

**.**

__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__political party or faction that seeks to form

**a**majority in

**a**parliament or on

**a**board

**of**directors or other responsible body typically must run

**a**full slate if only to demonstrate that they have the capacity to attract the talent to fill every position with some person, even if that person

**is**not

__ideal__for the job

**.**

__Any__mixture less than 14

**.**7 to 1

**is**considered to be

**a**rich mixture ; any more than 14

**.**7 to 1

**is**

**a**lean mixture – given perfect (

__ideal__) " test " fuel ( gasoline consisting

**of**solely n-heptane and iso-octane ).

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__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 R

__Any__subset

**of**

__R__< sup > n </ sup > ( with its subspace topology ) that

**is**homeomorphic to another open subset

**of**

__R__< sup > n </ sup >

**is**itself open

**.**

Brown continued releasing recordings: in 1993, he issued the album, Universal James, which included Brown's final Billboard charted single, " Can't Get

__Any__Harder ", which peaked at # 76 on the US__R__& B chart and # 59 on the UK chart**.**__Any__formal series with has

**a**composition inverse provided

**is**

**an**invertible element

**of**

__R__

**.**The coefficients are found recursively from the above formula for the coefficients

**of**

**a**composition, equating them with those

**of**the composition identity X ( that

**is**1 at degree 1 and 0 at every degree greater than 1 )

**.**

*****

__Any__positive multiple

**of**the repunit

__R__< sub > n </ sub >< sup >( b )</ sup > contains at least n nonzero digits in base b

**.**

__Any__binary relation

__R__on

**a**set A can generate

**a**natural partial order on the R-cycle equivalence classes

**of**set A, so that xRy implies ≥

**.**

*****The Drug War in Mexico: By

__Any__Other Name it's Terrorism, by Barnard

__R__

**.**Thompson ( MexiData

**.**info )

__Any__totally ordered set that

**is**not isomorphic to

__R__but satisfies ( 1 ) – ( 4 )

**is**known as

**a**Suslin line

**.**

__Any__physical object whose radius

__R__becomes less than or equal to the Schwarzschild radius will undergo gravitational collapse and become

**a**black hole

**.**

__Any__proposed inverse

__R__

**of**F ( reconstruction formula, in the lingo ) would have to map to some subset

**of**

**.**

*****

__Any__slave who evades capture for 20 days or more

**is**to be publicly whipped for the first offense ; branded with the letter

__R__on the right cheek for the second offense ; and lose one ear if absent for thirty days for the third offense ; and castrated for the fourth offense

**.**

In early June, Banks released the second single off the album, "

__Any__Girl " featuring__R__& B singer Lloyd**.**
O

**.**A**.**__R__., who grew up in nearby Rockville, Maryland, recorded the live album__Any__Time Now at the 9: 30 Club on November 23 – 24, 2001**.**__Any__non-singular matrix S

**of**the same size

**is**said to transform A into another symmetric matrix B = SAS < sup > T </ sup >, also

**of**order n, where S < sup > T </ sup >

**is**the transpose

**of**S

**.**If A

**is**the coefficient matrix

**of**some quadratic form

**of**

__R__< sup > n </ sup >, then B

**is**the matrix for the same form after the change

**of**coordinates defined by S

**.**

Lloyd C

**.**Gardner, " Pay__Any__Price: Lyndon Johnson and the Wars for Vietnam ", Chicago: Ivan__R__**.**Dee, 1995**.**0.430 seconds.