module categories造句
例句與造句
- This gives a well-defined functor \ Omega from the stable module category to itself.
- In modular representation theory of a finite group G, the stable module category is yet another example.
- One important property of the stable module category is it allows defining the ? functor for general rings.
- However, in general projective covers need not exist, and so passing to the stable module category is necessary.
- In practice one often considers hereditary finite dimensional algebras " A " because the module categories over such algebras are fairly well understood.
- It's difficult to find module categories in a sentence. 用module categories造句挺難的
- The module category is not semisimple, since one may induce a representation of the abelian Lie algebra where " b " 0 acts by a nontrivial Jordan block.
- The functor ? " 1 can even be defined on the module category of a general ring ( without factoring out projectives ), as the cokernel of the injective envelope.
- The vertex operator superalgebra is holomorphic, in the sense that all modules are direct sums of itself, i . e ., the module category is equivalent to the category of vector spaces.
- The advantage of this definition of " projective " is that it can be carried out in categories more general than module categories : we don't need a notion of " free object ".
- When " R " is semiperfect ), then ? ( " M " ) can be defined as the kernel of the projective cover, giving a functor on the module category.
- Some authors use the term "'module category "'for the category of modules; this term can be ambiguous since it could also refer to a category with a monoidal-category action.
- A cluster tilted algebra arises from a tilted algebra as a certain semidirect product, and the cluster category of " A " summarizes all the module categories of cluster tilted algebras arising from " A ".
- In fact the converse is also true and this gives a " characterization of division rings " via their module category : A unital ring " R " is a division ring if and only if every R-free.