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* Any commutative ring becomes a *- ring with the trivial involution.

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## 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 becomes

__Any__amendment so ratified

__becomes__

**a**valid part of

**the**Constitution, provided that no state " shall be deprived of its equal Suffrage in

**the**senate ," without its consent

**.**

__Any__handmade envelope is effectively

**a**lettersheet because prior to

**the**folding stage it offers

**the**opportunity for writing

**a**message on that area of

**the**sheet that after folding

__becomes__

**the**inside of

**the**face of

**the**envelope

**.**

*****

__Any__piece, save for

**the**king, may be captured and removed from

**the**board if it

__becomes__surrounded on two opposite sides by enemies

**.**

__Any__subsequent child born to

**the**couple

__becomes__

**the**half-sister or half-brother of

**the**prior children from previous relations

**.**

__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__dish

**with**huitlacoche must include

**a**slow simmer of

**the**fungus until it

__becomes__black which also removes most of

**the**starch of

**the**corn and what is left is

**a**black oily paste

**.**

__Any__subsystem that

__becomes__excessively loaded can compromise

**the**performance of other clients contending for that subsystem

**.**

__Any__anisotropic or isotropic linear algebraic group over

**a**field

__becomes__split over

**the**algebraic closure, so this distinction is interesting from

**the**point of view of Algebraic number theory

**.**

*****

__Any__U

**.**S

**.**financial institution that

__becomes__aware that it has possession of or control over funds in which

**a**designated FTO or its agent has an interest must retain possession of or control over

**the**funds and report

**the**funds to

**the**Office of Foreign Assets Control of

**the**U

**.**S

**.**Department of

**the**Treasury

**.**

"

__Any__large organization, Michels pointed out, has to create**a**bureaucracy in order to maintain its efficiency as it__becomes__larger — many decisions have to be made daily that cannot be made by large numbers of disorganized people**.**__Any__object she sits on or lies upon during this period

__becomes__

**a**midras l ' tumah ( carrier of tumah ).

__Any__skew semistandard tableau of shape /

**with**positive integer entries gives rise to

**a**sequence of partitions ( or Young diagrams ), by starting

**with**, and taking for

**the**partition places further in

**the**sequence

**the**one whose diagram is obtained from that of by adding all

**the**boxes that contain

**a**value ≤ in ; this partition eventually

__becomes__equal to

**.**

__Any__time

**a**new release is added or old release edited, that entry

__becomes__flagged as needing " votes " ( initially, " review ," but this term caused confusion ).

__Any__Taelon who

__becomes__disconnected from

**the**Commonality ( which has happened on at least one occasion ) reverts back to an Atavus,

**with**

**the**reappearance of

**the**dormant Shaqarava

**.**

__Any__device

**with**its Bluetooth connection turned on and set to " discoverable " ( able to be found by other Bluetooth devices in range ) may be susceptible to Bluejacking, and possibly to Bluesnarfing when, and if, Bluesnarfing of

**the**current Bluetooth security

__becomes__possible

**.**

__Any__point of location

__becomes__frequented / enlivened / vivified not merely by

**the**passing by visits but when people gather and stay there for

**a**duration

**.**

__Any__sequence space can also be equipped

**with**

**the**topology of pointwise convergence, under which it

__becomes__

**a**special kind of Fréchet space called FK-space

**.**

__Any__child born to

**a**married woman, even if she is known to have been unfaithful, is presumed to be her husband's, unless she is so promiscuous that such

**a**presumption

__becomes__unsupportable ,( Shulhan Arukh Even haEzer 4: 15 ) or if she enters

**a**public relationship

**with**another man ( 4: 16 ).

__Any__flat wheel that

__becomes__too dangerous to travel on (

**a**big flat spot on

**the**train wheel ) will be counted as

**a**defect

**.**

1.562 seconds.