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* Any commutative ring R is an algebra over itself, or any subring of R.

from
Wikipedia

## Some Related Sentences

Any and commutative

*****

__Any__

**ring**

**of**matrices with coefficients in a

__commutative__

**ring**

**R**forms

**an**R-algebra under matrix addition and multiplication

**.**

__Any__

__commutative__monoid

**is**endowed with its algebraic preordering ≤, defined by x ≤ y if and only if there exists z such that x + z = y

**.**

__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__linear transformation f: V → A from V to**an****algebra**A**over**K can be uniquely extended to**an****algebra**homomorphism from T ( V ) to A as indicated by the following__commutative__diagram:*****

__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__

__commutative__semigroup

**is**a medial magma

**,**and a medial magma has

**an**identity element if and only if it

**is**a

__commutative__monoid

**.**

__Any__affine group scheme

**is**the spectrum

**of**a

__commutative__Hopf

**algebra**(

**over**a base S

**,**this

**is**given by the relative spectrum

**of**

**an**O < sub > S </ sub >-

**algebra**).

__Any__complete group variety ( variety here meaning reduced and geometrically irreducible separated scheme

**of**finite type

**over**a field )

**is**automatically

__commutative__

**,**by

**an**argument involving the action

**of**conjugation on jet spaces

**of**the identity

**.**

__Any__

__commutative__

**algebra**

**is**a supercommutative

**algebra**if given the trivial gradation ( i

**.**e

**.**all elements are even ).

Any and ring

__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__

__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__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**.**0.421 seconds.