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Page "Modular representation theory" ¶ 56
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Indeed and if
Indeed, if pressed, we would say what the late Robert Henri, American painter, said to a pupil, `` Anything will do for a subject: it's what you do with it that counts ''.
Indeed, one such clause can be rewritten as, that is, if are all true, then y needs to be true as well.
Indeed, the expert system quickly developed in front of the expert shows him if the future application should be programmed.
Indeed, after something like thirty years ' experience of international conferences of one kind and another, if I had to pick a team for going into a conference room, Stalin would be my first choice.
Indeed it has been noted it is difficult if not impossible to define one category without contrasting it with the other.
Indeed it was argued that, if the nature of reality itself was in question, and if previous restrictions which had been in place around human activity were dissolving, then art, too, would have to radically change.
Indeed, in 1603 Johann Bayer gave three of these clusters designations as if they were single stars.
Indeed, even if the photoelectric effect is the favoured reaction for a particular single-photon bound-electron interaction, the result is also subject to statistical processes and is not guaranteed, albeit the photon has certainly disappeared and a bound electron has been excited ( usually K or L shell electrons at nuclear ( gamma ray ) energies ).
Indeed, if a husband had no natural brothers, he would adopt another man to be his brother so that he would be allowed to marry.
Indeed, if x and y are integers satisfying this equation, then x / y is an approximation of √ 2.
" Indeed, Diodorus goes so far as to say that " But if any man, putting envy aside, will estimate closely not only the man's natural gifts but also his achievements, he will find that on both counts Themistocles holds first place among all of whom we have record.
Indeed, if ( A, φ ) is an initial morphism and k: A → A ′ is any isomorphism then the pair ( A ′, φ ′), where φ ′ =
Indeed, if the sapling dies, the mature tree gains nutrients from the decaying sapling.
As historian Richard Lane concludes, " Indeed, if there is one work that made Hokusai's name, both in Japan and abroad, it must be this monumental print-series ...".
Indeed, a totally ordered set ( with its order topology ) is compact as a topological space if it is complete as a lattice.
Indeed, those who refused to leave were generally removed from their barracks, sometimes by force, even if they had no place to go.
Indeed, a set is nowhere dense if and only if its closure is nowhere dense.
) Indeed, if a space is Hausdorff then it is T < sub > 0 </ sub >, and each T < sub > 0 </ sub > regular space is Hausdorff: given two distinct points, at least one of them misses the closure of the other one, so ( by regularity ) there exist disjoint neighborhoods separating one point from ( the closure of ) the other.
Indeed, if the order the winning cards are placed is fixed it is possible to create an infinite loop wherein neither side will win and the game will not end.
Indeed, even if the interest of the bonds it holds ( for example ) is paid semi-annually, the value of its book of bond will increase daily, thanks to accrued interest being accounted for, and therefore the bank will be able to re-invest these daily accrued interest ( by lending additional money or buying more financial products ).
Indeed if:, and
Observe first the following: if a is a limit point of S, then any finite collection C of open sets, such that each open set U ∈ C is disjoint from some neighborhood V < sub > U </ sub > of a, fails to be a cover of S. Indeed, the intersection of the finite family of sets V < sub > U </ sub > is a neighborhood W of a in R < sup > n </ sup >.
Indeed, the effect was quite the contrary, psychology began to thrive: " perhaps, in the early days of scientific progress, a subject often grows all the more surely if its workers have to meet difficulties, improvise their apparatus, and rub very close shoulders one with another.

Indeed and simple
Indeed, until recently, it was believed that the development of technology was restricted only to human beings, but recent scientific studies indicate that other primates and certain dolphin communities have developed simple tools and learned to pass their knowledge to other generations.
Indeed, Brown I itself did not need to rely upon any psychological or social-science research in order to announce the simple, yet fundamental truth that the Government cannot discriminate among its citizens on the basis of race.
Indeed, in 1815 at the age of sixty-four Charles Emmanuel took simple vows in the Society of Jesus ( the Jesuits ).
Indeed, a slightly cryptic but essentially simple idiom allows this to be done by the program itself as it is running, producing self-modifying code.
Indeed, traditional foods tend to be simple, utilising readily-available ingredients and those cuts of meat that were not readily saleable.
Indeed, much of the political tension in modern societies is the conflict between the desire to organize a nation-state using the tribal values of egalitarianism and unity and the simple fact that large societies are unavoidably impersonal and sometimes not amenable to small-society rules.
A very useful fact about these topologies is that we may exhibit a basis for them consisting of particularly simple elements, namely the D ( f ) for individual polynomials ( or for projective varieties, homogeneous polynomials ) f. Indeed, that these form a basis follows from the formula for the intersection of two Zariski-closed sets given above ( apply it repeatedly to the principal ideals generated by the generators of ( S )).
Indeed, this is one of the reasons why edge detection may be a non-trivial problem unless the objects in the scene are particularly simple and the illumination conditions can be well controlled ( see for example, the edges extracted from the image with the girl above ).
Indeed, it is a song of joy and wonder at the beauty of nature in simple actions like birdsong and dew on the grass.
Indeed, the compact operators on a Hilbert space form a maximal ideal, so the quotient algebra, known as the Calkin algebra, is simple.
Indeed, it is a simple matter to explain away all allegedly unselfish motives " He quotes Lucius F. C. Garvin to this effect: " Once the conviction that selfishness is universal finds root in a person's mind, it is very likely to burgeon out in a thousand corroborating generalizations.
Indeed, a simple way to think about a two-plane light field is as a collection of perspective images of the st plane ( and any objects that may lie astride or beyond it ), each taken from an observer position on the uv plane.
Indeed, her words are perfectly chosen, easy to understand, and deceptively simple.
Indeed, as a general rule, most character datasets are so " noisy " that no truly " simple " solution is possible.
Indeed, local hardware stores would often sell inexpensive chain cut to length using simple bolt cutters.
Indeed, in a criticism of Adam Smith, Marx specifically refers to the law of value governing " simple commodity exchange "-the point being that this law is transformed in capitalist exchange where " more labour is exchanged for less labour ( from the labourer ’ s standpoint ), less labour is exchanged for more labour ( from the capitalist ’ s standpoint )".
Indeed, Utopia has many of the characteristics of satire, and there are many jokes and satirical asides such as how honest people are in Europe, but these are usually contrasted with the simple, uncomplicated society of the Utopians.

Indeed and module
In fact this is an example of a bimodule, and it may be possible for an abelian group M to be made into a left-R, right-S bimodule for a different ring S. Indeed, for any right module M, it is automatically a left module over the ring of integers Z, and moreover is a Z-R bimodule.
Indeed, the global dimension of regular local rings is finite, i. e. any finitely generated module has a finite projective resolution, so the canonical map K < sub > 0 </ sub > → G < sub > 0 </ sub > is surjective.
Indeed, if language were a module it would be informationally encapsulated.

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