Help


[permalink] [id link]
+
Page "Homology (mathematics)" ¶ 29
from Wikipedia
Edit
Promote Demote Fragment Fix

Some Related Sentences

If and we
If we let them go, they won't stay away, they'll find men to ride with them and they'll be back.
If we was both armed, you wouldn't talk so tough ''.
If we have to we'll take him apart and see what he's made of ''!!
If we look at recent art we find it preoccupied with form.
If we were creating a wholly new society, we could insist that our social, political, economic and philosophic institutions foster rather than hamper man ; ;
If we want respect from ourselves or others, we will have to earn it.
If we cannot stop warfare in our own economic system, how can we expect to abolish it internationally??
If we examine the three types of change from the point of view of their internal structure we find an additional profound difference between the third and the first two, one that accounts for the notable difference between the responses they evoke.
If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??
If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.
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.
If you had screamed right there in the street where we stood, I could not have felt more fear.
If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.
If we grasp this opportunity to build an age of productive partnership between the less fortunate nations and those that have already achieved a high state of economic advancement, we will make brighter the outlook for a world order based upon security and freedom.
If art is to release us from these postulated things ( things we must think symbolically about ) and bring us back to the ineffable beauty and richness of the aesthetic component of reality in its immediacy, it must sever its connection with these common sense entities ''.
If he's going to the St. Louis convention as a delegate we ought to know it.
If we are to believe the list of titles printed in Malraux's latest book, La Metamorphose Des Dieux, Vol. 1 ( ( 1957 ), he is still engaged in writing a large novel under his original title.
If we break the minister to our bit, we are buying back our own sins.

If and take
If you take the one, you'd better take both ''.
Without preliminaries, Esther asked him, `` If you are a world citizen, will you take Garry Davis' place in his tent while he goes to the hospital ''??
If his circumspection in regard to Philip's sensibilities went so far that he even refused to grant a dispensation for the marriage of Amadee's daughter, Agnes, to the son of the dauphin of Vienne -- a truly peacemaking move according to thirteenth-century ideas, for Savoy and Dauphine were as usual fighting on opposite sides -- for fear that he might seem to be favoring the anti-French coalition, he would certainly never take the far more drastic step of ordering the return of Gascony to Edward, even though, as he admitted to the English ambassadors, he had been advised that the original cession was invalid.
If you're lyin' out in the hammock at night, and it gets kinda cool -- you know -- you just take these sides with the fringe on -- see -- and wrap 'em right over you.
If Russian pupils have to take these languages, how come American students have a choice whether or not to take a language, but have to face so many exceptions??
If this practice should take root and spread, the man who submits a manuscript to a publisher will find himself reviewed before he is accepted and publication will become a sort of post-mortem formality.
If the Department of State is to take primary responsibility for foreign policy in Washington, it follows that the ambassador is expected to take charge overseas.
If our national interest lies in being able to fight and win a war rather than committing national suicide, then we must take a much more penetrating look at ballistic missiles.
If companies will take the time to give objective consideration to their major problems and to the questions they provoke, then a long constructive step will have been taken toward more effective marketing in next decade.
If such an unlikely transaction were to take place, it would more logically be accomplished by a stock purchase, followed by the prosecution of the claim by the wholly-owned subsidiary, followed by liquidation.
If we were asked why we thought so, we should say that these things involve great evil and are wrong, and that to take delight in what is evil or wrong is plainly unfitting.
If it is owned, taxes must be paid, and if the place is not free of mortgage, there will be interest and payments on the principal to take care of.
If you're really serious about working on that story, I'd better take you home ''.
If you want my advice, pack up and take the next train back to New York ''.
If you draw the short straw I'll lend you some bread, like fifty bucks, before I take off to visit my sister in Frisco.
If they have to take any car, they'd rather take the big one.
If any among the hardy hundreds who sat in the downpour are in doubt about how it comes out, let them take comfort.
If she could not take the children out of this section, at least she could take other children out of their countries and put them on the farms.
I kept saying, `` If I could just build up a reputation for myself, make some real money, get to be well known as an illustrator -- like Peter Askington, for instance -- then I could take some time off and paint ''.

If and modules
If k is a field and G is a group, then a group representation of G is a left module over the group ring k. The simple k modules are also known as irreducible representations.
* If R is a ring, then the category of all left ( or right ) modules over R is an abelian category.
* If R is a left-noetherian ring, then the category of finitely generated left modules over R is abelian.
Let V and W be vector spaces ( or more generally modules ) and let T be a linear map from V to W. If 0 < sub > W </ sub > is the zero vector of W, then the kernel of T is the preimage of the zero subspace
If a system is to be built from existing system, this approach is more suitable as it starts from some existing modules.
The latter example leads to a generalization of modules over rings: If C is a preadditive category, then Mod ( C ) := Add ( C, Ab ) is called the module category over C. When C is the one-object preadditive category corresponding to the ring R, this reduces to the ordinary category of ( left ) R-modules.
If we interpret the object as the left module, then this matrix category becomes a subcategory of the category of left modules over.
If the chain complex depends on the object X in a covariant manner ( meaning that any morphism X → Y induces a morphism from the chain complex of X to the chain complex of Y ), then the H < sub > n </ sub > are covariant functors from the category that X belongs to into the category of abelian groups ( or modules ).
If cryptographic modules were to be signed in multiple locations, using multiple keys is a reasonable approach.
If one module misbehaves in a chain of interrelated modules, it is not so immediately clear where to look for the cause of the failure.
If there is some notion of " localization " which can be carried over to modules, such as is given at localization of a ring, one can define locally free modules, and the projective modules then typically coincide with the locally free ones.
* If X is a smooth proper scheme over a field K then the ℓ-adic cohomology groups of its geometric fibre are Galois modules for the absolute Galois group of K.
If M and N are two simple modules over a ring R, then any homomorphism f: M → N of R-modules is either invertible or zero.
If are two coherent algebraic sheaves on and if is a map of sheaves of modules then there exists a unique map of sheaves of modules with f =
If is a coherent analytic sheaf of modules over X < sup > an </ sup > then there exists a coherent algebraic sheaf of-modules and an isomorphism.
If C is locally small, satisfies Grothendieck's axiom AB5 ) and has enough injectives, then every object in C has an injective hull ( these three conditions are satisfied by the category of modules over a ring ).
If is an arbitrary integral weight, it is in fact a large unsolved problem in representation theory to describe the cohomology modules in general.
If the modules M < sub > 1 </ sub > and M < sub > 2 </ sub > have finite length, then so does their direct sum, and the length of the direct sum equals the sum of the lengths of M < sub > 1 </ sub > and M < sub > 2 </ sub >.
If the algebra is not unital, it may be made so in a standard way ( see the adjoint functors page ); there is no essential difference between modules for the resulting unital ring, in which the identity acts by the identity mapping, and representations of the algebra.
Let R be a ring, and let M, P be modules over R. If i: P → M is injective then P is a pure submodule of M if, for any R-module X, the natural induced map on tensor products i ⊗ id < sub > X </ sub >: P ⊗ X → M ⊗ X is injective.
NOTE: If you want to test these examples on your own, you should start Maude with the option-no-prelude which lets Maude know that none of its basic modules are included ( like Maude's own NAT module which will cause a conflict ).

0.235 seconds.