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Page "Weyl algebra" ¶ 25
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fact and is
In fact, one important aspect of their very religion is the annihilation of men ''.
In fact it has caused us to give serious thought to moving our residence south, because it is not easy for the most objective Southerner to sit calmly by when his host is telling a roomful of people that the only way to deal with Southerners who oppose integration is to send in troops and shoot the bastards down.
The fact is due mainly to international wars, both hot and cold.
While the pattern is uneven, some having gained more than others, nationalism has in fact served the Western peoples well.
In point of fact, this is a beige box with a bright red door, about one and a half feet square and hung from the wall about six feet from the door to Wisman's right.
The fact is that the Southern Confederacy differed from the earlier one almost as much as the Federal Constitution did.
To my knowledge, Lincoln remains the only Head of State and Commander-in-Chief who, while fighting a fearful war whose issue was in doubt, proved man enough to say this publicly -- to give his foe the benefit of the fact that in all human truth there is some error, and in all our error, some truth.
In fact the accumulation of the hardware of destruction is day by day increasing our fear of each other.
The new fact the initiates of this cult have to learn is that they must move toward simplicity.
The magic circle is, in fact, a symbol of and preparation for the metaphysical orgasm ''.
Operating as a one man police force in fact if not in name, he is at once more independent and more dedicated than the police themselves.
`` I may possibly be a greater risk than is the normal person of my age '', the President had said on February 29th of the election year, ignoring the fact that no one of his age had ever lived out another term.
In the incessant struggle with recalcitrant political fact he learns to focus the essence of a problem in the significant detail, and to articulate the distinctions which clarify the detail as significant, with what is sometimes astounding rapidity.
we accord it its place there, and in Lawrence's treatment we are given the innocent fantasy of a child, in fact, the form in which oedipal love is expressed in childhood.
There is probably some significance in the fact that two of the best incest stories I have encountered in recent years are burlesques of the incest myth.
How much they esteemed him is shown by the fact that their underground committee selected him as one of the few who would be helped to escape.
That is not to deny that he has been aware of traditions, of course, that he is steeped in them, in fact, or that he has dealt with them, in his books.
There is evidence to suggest, in fact, that many authors of the humorous sketches were prompted to write them -- or to make them as indelicate as they are -- by way of protesting against the artificial refinements which had come to dominate the polite letters of the South.
It seems quite obvious that all the really difficult tasks of human beings arise from the fact that man is not one, but many.
If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.
Perhaps the mere fact that by plucking on the nerves nature can awaken in the most ordinary of us, temporarily anyway, the sleeping poet, and in poets can discover their immortality, is the most remarkable of all the remarkable phenomena to which we can attest??

fact and module
% This is the file ' fact. erl ', the module and the filename must match
In fact, at least one quest in this module still has the original NPC's name, unchanged.
Since a one sided maximal ideal A is not necessarily two-sided, the quotient R / A is not necessarily a ring, but it is a simple module over R. If R has a unique maximal right ideal, then R is known as a local ring, and the maximal right ideal is also the unique maximal left and unique maximal two-sided ideal of the ring, and is in fact the Jacobson radical J ( R ).
In fact, it turns out that ( for a Noetherian ring ) the set is precisely the assassinator of the module R / I ; that is, the set of all annihilators of R / I ( viewed as a module over R ) that are prime.
In fact, is a module over the Iwasawa algebra ( i. e. the completed group ring of over ).
The covariant derivative can also be constructed from the Cartan connection η on P. In fact, constructing it in this way is slightly more general in that V need not be a fully fledged representation of G. Suppose instead that that V is a (, H )- module: a representation of the group H with a compatible representation of the Lie algebra.
RTLinux is in fact a Linux kernel module.
) This follows from the fact that R has a maximal left ideal M, and the fact that the quotient module R / M is a simple left R-module, and that its annihilator is a proper two-sided ideal in R. Since R is a simple ring, this annihilator is
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.
This is in fact a special case of the version above, since every K-linear representation of a group G can be viewed as a module over the group algebra KG.
In fact, since any rep of G can be thought of as a module for C and vice versa, we can look at the center of C. This is analogous to looking at the center of the universal enveloping algebra of a Lie algebra.
To avoid the possible confusion with the regular rings and regular local rings of commutative algebra ( which are unrelated notions ), von Neumann regular rings are also called absolutely flat rings, because these rings are characterized by the fact that every left module is flat.
Astronauts, managers and various members of the press all complained that the benefits of the program were outweighed by the risks associated with it, especially considering the fact that most of the US science experiments had been contained within the holed module.
The multiplicity of a projective indecomposable module as a summand of the group algebra ( viewed as the regular module ) is the dimension of its socle ( for large enough fields of characteristic zero, this recovers the fact that each simple module occurs with multiplicity equal to its dimension as a direct summand of the regular module ).
In Peru, Dr. Linnea Smith reports, " despite the fact that the state nursing course book admits that no evidence has ever been produced to document the effectiveness of the black stone, each student is required to make ... one ... as a part of the first aid module.
Based on this fact he introduced a vectorial way to describe any rotation, with a vector on the rotation axis and module equal to the value of the angle.
The reputation of the CIJWS lies in the fact that the training module is framed in a highly scientific manner-soldiers receive training in identifying improvised explosive devices ( IED ), jungle survival, counter terrorism, and interrogation techniques.

fact and over
The fact that he has cast over those materials the light of a skeptical mind does not make him any the less Southern, I rather think, for the South has been no more solid than other regions except in the political and related areas where patronage and force and intimidation and fear may produce a surface uniformity.
To you, for instance, the word innocence, in this connotation, probably retained its Biblical, or should I say technical sense, and therefore I suppose I must make myself quite clear by saying that I lost -- or rather handed over -- what you would have considered to be my innocence two weeks before I was legally entitled, and in fact by oath required, to hand it over along with what other goods and bads I had.
In fact, over the years, the American farmer's capacity to over-produce has cost the taxpayers a large dollar.
The publication last July of the party's Draft Program -- that blueprint for the `` transition to communism '' -- had led the uninitiated to suppose that this Twenty-second Congress would be a sort of apotheosis of the Khrushchev regime, a solemn consecration of ideas which had, in fact, been current over the last three or four years ( i.e., since the defeat of the `` anti-party group '' ) in all theoretical party journals.
In spite of the fact that the state legislature voted us neutral, John Hunt Morgan is openly flying the Confederate flag over his woolen factory ''!!
Fundamental to the difficulty of creating the desired prestige is the fact that, in the business community, prestige and status are conferred in proportion to the authority that one man has over others and the extent of which he participates in the management functions ''.
This has survived the years but there has been considerable concern among the tenants over the fact that the oil was not metered.
The joint investigations of linguistics and psychiatry have established, in point of fact, that no matter what the subject of conversation is or what words are involved, it is impossible for people to talk at all without telling over and over again what sort of people they are and how they relate to the rest of the world.
In fact all of our civilized world is the resultant of man's projection of his imagination over the past 60 centuries or more.
`` All too frequently '', points out James O'Gara, managing editor of Commonweal, `` Catholics run roughshod over Protestant sensibilities in this matter, by failure to consider the reasoning behind the Protestant position and, particularly, by their jibes at the fact that Protestant opinion on birth control has changed in recent decades ''.
A study of major denominational membership statistics over a twenty-year period revealed the appalling fact that nearly 40 per cent of those who joined the Church were lost to the Church within seven years.
Morals aside, the fat man has plenty to worry about -- over and above the fact that no one any longer loves him.
But there was no getting over the fact that his father had sworn to pardon him and let him live in peace if he returned to Russia.
Additionally, the claimants to this ancestry also claim descendancy from Sargon of Akkad ( whose dynasty died out over 1500 years before the Assyrian dynasty fell ), and from Nabopolassar, who was a Chaldean, politically and militarily opposed to Assyria, and not in fact an Assyrian.
Despite the fact that four of his sons ( Aban, Abd al Rahman, Muhammad and Ahmad ) were alive at the time of his death, all of them were passed over for succession.
In point of fact, Capp maintained creative control over every stage of production for virtually the entire run of the strip.
Habakkuk addresses his concerns over the fact that God will use the evil Babylonian empire to execute judgment on Judah for their sins.
The company had re-leased estimates covering 20 % damage to be re-insured at minimal fees when in fact the damage was over 65 % and every claim was in the millions.
The importance of foodcrops over exported cash crops is illustrated by the fact that the total production of cassava, the staple food of most Central Africans, ranges between c. 200, 000 and 300, 000 tons a year, while the production of cotton, the principal exported cash crop, ranges from c. 25, 000 to 45, 000 tons a year.
In fact, this very story, along with some hints from " The Shadow over Innsmouth ", provides the key to the origin of the ' Derleth Mythos '.
However, none of these parameters differ significantly from early writings of Howard and Balfour, suggesting that in fact modern composting has not made significant advances over the traditional methods that take a few months to work.
The new nation was defined as consisting of the entire archipelago, despite the fact that France maintains control over Mayotte.
The relative moderation of Constantius ' actions toward paganism is reflected by the fact that it was not until over 20 years after Constantius ' death, during the reign of Gratian, that any pagan senators protested their religion's treatment.

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