例句與造句

1. Tor is defined using a projective resolution of its first argument.
2. Projective resolutions ( and, more generally, flat resolutions ) can be used to compute Tor functors.
3. For projective resolutions, this condition is almost invisible : a projective pre-cover is simply an epimorphism from a projective module.
4. At each stage of the induction, the properties of projective objects are used to define maps in a projective resolution of A.
5. However, projective covers need not exist in general, so minimal projective resolutions are only of limited use over rings like the integers.
6. It's difficult to find projective resolution in a sentence. 用projective resolution造句挺難的
7. If " M " does not admit a finite projective resolution, then by convention the projective dimension is said to be infinite.
8. Since flat covers exist for all modules over all rings, minimal flat resolutions can take the place of minimal projective resolutions in many circumstances.
9. There is also a projective resolution between circular and hyperbolic cases : both curves are conic sections, and hence are treated as projective ranges in projective geometry.
10. These ideas are also familiar from the more common notion of minimal projective resolutions, where each map is required to be a projective cover of the kernel of the map to the right.
11. The measurement of the departure of flat resolutions from projective resolutions is called " relative homological algebra ", and is covered in classics such as and in more recent works focussing on flat resolutions such as.
12. These Ext groups can also be computed via a projective resolution of "'Z "', the advantage being that such a resolution only depends on " G " and not on " M ".
13. In particular, the sequence x _ 1, \ ldots, x _ n is regular, and the Koszul complex is thus a projective resolution of k = R / \ langle x _ 1, \ ldots, x _ n \ rangle.
14. In particular, every module has "'free resolutions "', "'projective resolutions "'and "'flat resolutions "', which are left resolutions consisting, respectively of free modules, projective modules or flat modules.
15. The dual concept, "'projective sheaves "', is not used much, because in a general category of sheaves there are not enough of them : not every sheaf is the quotient of a projective sheaf, and in particular projective resolutions do not always exist.
16. It was Jean-Pierre Serre who found a homological characterization of regular local rings : A local ring " A " is regular if and only if " A " has finite global dimension, i . e . if every " A "-module has a projective resolution of finite length.
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