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Conversely in rings with unity, any simple left R module arises this way.

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## Some Related Sentences

Conversely and rings

__Conversely__

**,**given central idempotents a < sub > 1 </ sub >,..., a < sub > n </ sub >

**in**

**R**that are pairwise orthogonal and have sum 1

**,**then

**R**is the direct sum of the

__rings__Ra < sub > 1 </ sub >,…, Ra < sub > n </ sub >.

__Conversely__

**,**

**in**the category of

__rings__

**,**there are no kernels

**in**the category-theoretic sense ; indeed

**,**

**this**category does not even have zero morphisms

**.**

Conversely and with

__Conversely__

**,**British English favours fitted as the past tense of fit generally

**,**whereas the preference of American English is more complex: AmEng prefers fitted for the metaphorical sense of having made an object " fit " ( i

**.**e., suited ) for a purpose ;

**in**spatial transitive contexts

**,**AmEng uses fitted for the sense of having made an object conform to an unchanged object that it surrounds ( e

**.**g., " fitted X around Y ") but fit for the sense of having made an object conform to an unchanged object that surrounds it ( e

**.**g., " fit X into Y "); and for the spatial senses ( both intransitive and transitive ) of having been matching

__with__respect to contour

**,**

__with__no alteration of either object implied

**,**AmEng prefers fit (" The clothes fit

**.**

__Conversely__

**,**paintings which came out of his workshop that were not necessarily physically worked on by Cuyp but merely overseen by him technically

**,**were marked

__with__A

**.**C

**.**to show that it was his instruction which saw the paintings ’ completion

**.**

__Conversely__

**,**the existence of Bletchley Park

**,**and of the decrypting achievements there

**,**was never officially shared

__with__the Soviet Union

**,**whose war effort would have greatly benefited from regular decrypting of German messages relating to the Eastern Front

**.**

__Conversely__

**,**the islands do not receive the upwellings ( cold streams ) that affect the West African coast

**,**so the air temperature is cooler than

**in**Senegal

**,**but the sea is actually warmer

**,**because the orographic relief of some islands

**,**as Sao Miguel

__with__steep mountains

**,**cover it

__with__rich woods and luxuriant vegetation where the dense moisture condense and soak the plants

**,**rocks

**,**soil

**,**logs

**,**moss etc

**.**

__Conversely__

**,**an absence of secure cycle-parking is a recurring complaint by cyclists from cities

__with__low modal share of cycling

**.**

__Conversely__

**,**states such as Virginia and Massachusetts

**in**the United States of America did not have sovereign status

**,**but had significant political and economic independence coupled

__with__weak federal control

**,**reducing the incentive to secede

**.**

__Conversely__

**,**

**in**the English language as a whole

**,**singular verb forms can often be used

__with__nouns ending

**in**"- s " that were once considered plural ( for example: " Physics is my favorite academic subject ").

__Conversely__the car is stopped by releasing pressure on the cable (

__with__or without completely detaching ) and applying the brakes

**.**

__Conversely__

**,**a column

__with__a low reflux ratio must have a large number of stages

**,**thus requiring a taller column

**.**

__Conversely__

**,**factors that favor plate columns are: presence of solids

**in**feed

**,**high liquid rates

**,**large column diameters

**,**complex columns

**,**columns

__with__wide feed composition variation

**,**columns

__with__a chemical reaction

**,**absorption columns

**,**columns limited by foundation weight tolerance

**,**low liquid rate

**,**large turn-down ratio and those processes subject to process surges

**.**

__Conversely__

**,**

**in**functional code

**,**the output value of a function depends only on the arguments that are input to the function

**,**so calling a function f twice

__with__the same value for an argument x will produce the same result f ( x ) both times

**.**

__Conversely__

**,**given a groupoid G

**in**the algebraic sense

**,**let G < sub > 0 </ sub > be the set of all elements of the form x * x < sup >− 1 </ sup >

__with__x varying through G and define G ( x * x < sup >-1 </ sup >, y * y < sup >-1 </ sup >) as the set of all elements f such that y * y < sup >-1 </ sup > * f * x * x < sup >-1 </ sup > exists

**.**

__Conversely__

**,**Groups incur penalties when attempting to control Groups

__with__opposite alignments or when attempting to destroy groups

__with__the same alignment

**.**

__Conversely__

**,**John Calvin

**,**Albert Barnes Adam Clarke

**,**John Gill

**,**and John Wesley amongst many other have affirmed

**this**as divine truth and found no problem

__with__its historicity

**.**

__Conversely__

**,**JPL

**,**through the Caltech lawyers representing the laboratory

**,**allege that Coppedge's termination was simply due to budget cuts and his demotion from team lead was because of harassment complaints and from on-going conflicts

__with__his co-workers

**.**

__Conversely__

**,**Henig acknowledges that if the US had been a member

**,**its reluctance to engage

**in**war

__with__European states and to enact economic sanctions may have hampered the ability of the League to deal

__with__international incidents

**.**

__Conversely__

**,**simply having negative relationships

__with__some women does not necessarily mean someone holds misogynistic views

**.**

Conversely and unity

__Conversely__

**,**the rejection of syncretism

**,**usually

**in**the name of " piety " and " orthodoxy ", may help to generate

**,**bolster or authenticate a sense of uncompromised cultural

__unity__

**in**a well-defined minority or majority

**.**

__Conversely__

**,**ascending transformation increases the modulus towards

__unity__

**,**while decreasing the amplitude

**.**

Conversely and any

__Conversely__

**,**a subset

**R**defines a binary function if and only if

**,**for

__any__x

**in**X and y

**in**Y

**,**there exists a unique z

**in**Z such that ( x

**,**y

**,**z ) belongs to

**R**

**.**

__Conversely__the equilibrium position is said to be " far to the

**left**" if hardly

__any__product is formed from the reactants

**.**

* The spectrum of

__any__bounded linear operator on a Banach space is a nonempty compact subset of the complex numbers C**.**__Conversely__**,**__any__compact subset of C**arises****in****this**manner**,**as the spectrum of some bounded linear operator**.**__Conversely__

**,**there are other stars that never rise above the horizon

**,**as seen from

__any__given point on the Earth's surface ( except exactly on the equator ).

__Conversely__

**,**

__any__surjection between sets determines a partition on its domain

**,**the set of preimages of singletons

**in**the codomain

**.**

__Conversely__

**,**Derek Bickerton and others argue that the advent of abstract words provided a mental basis for analyzing higher-order relations

**,**and that

__any__communication system that remotely resembles human language utterly relies on cognitive architecture that co-evolved alongside language

**.**

__Conversely__

**,**a person may feel like he belongs to one state without having

__any__legal relationship to it

**.**

__Conversely__

**,**the interior of the box has a constant

**,**zero potential energy .< ref > Actually

**,**

__any__constant

**,**finite potential can be specified within the box

**.**

__Conversely__

**,**extremely thin jewelry can cause the same tearing

**in**what is commonly referred to as the " cheese cutter effect ", either during sudden torsion or over a long period of wearing

**,**especially if the thin jewelry bears

__any__weight

**.**

__Conversely__

**,**

__any__Hermitian positive semidefinite matrix M can be written as M = A < sup >*</ sup > A ;

**this**is the Cholesky decomposition

**.**

__Conversely__

**,**if a double sharp were added to

__any__other note not containing a sharp or flat as indicated by the key signature then the note will be raised two semitones or a whole step

**with**respect to the chromatic scale

**.**

__Conversely__

**,**supplementation

**with**L-phenylalanine

**,**L-tyrosine

**,**L-DOPA

**,**or

__any__of the cofactors will increase their respective concentrations

**.**

__Conversely__

**,**

__any__choice of μ

**,**full rank matrix U

**,**and positive diagonal entries Λ < sub > i </ sub > yields a non-singular multivariate normal distribution

**.**

__Conversely__

**,**the influence of the data at

__any__given point on the initial line propagates

**with**the finite velocity c: there is no effect outside a triangle through that point whose sides are characteristic curves

**.**

__Conversely__

**,**given

__any__harmonic function

**in**two dimensions

**,**it is the real part of an analytic function

**,**at least locally

**.**

__Conversely__

**,**if the Turing Machine is expected polynomial-time ( for

__any__given x ), then a considerable fraction of the runs must be polynomial-time bounded

**,**and the coin sequence used

**in**such a run will be a witness

**.**

It is a fact that the ring is a principal ideal ring ; that is

**,**for__any__ideal I**in****,**there exists an integer n**in**I such that every element of I is a multiple of n**.**__Conversely__**,**the set of all multiples of an arbitrary integer n is necessarily an ideal**,**and is usually denoted by ( n ).0.182 seconds.