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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, if the same is done with the left hand, a left-handed system results.
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, many natural forces, such as the sun, were associated with multiple deities.
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, wages tend to go up with a decrease in population.
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, let G be any polynomial such that Af.
Conversely, any algebra whose associator is alternating is clearly alternative.
Conversely, any algebra for which this is true is clearly alternative.
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, corresponding to any partition of X, there exists an equivalence relation ~ on X.
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 any planar graph can be formed from a map in this way.
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, in the absence of spatial continuity can take any value.
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 ).

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