homological in Czech
homological
Sentence patterns related to "homological"
1. Cluster Algebras homological algebra quivers representation theory triangulated categories
2. Homological Connectivity, a property related to the homology groups of a topological space.
3. He has established classic theorems concerning Cohen-Macaulay rings, invariant theory and homological algebra.
4. Stammbach's research deals with homological algebra, specifically with its applications to group theory ( homology and cohomology of groups).
5. The snake lemma is valid in every abelian category and is a crucial tool in homological algebra and its applications, for instance in algebraic topology.
6. Alexander Grothendieck (1957) Revolutionized homological algebra by introducing abelian categories and providing a general framework for Cartan and Eilenberg's notion of derived functors.
7. A straightforward result in homological algebra states that a chain complex with each free is Acyclic if and only if there exists a chain contraction.
8. He played a role in the beginnings of modern homotopy theory perhaps analogous to that of Saunders Mac Lane in homological algebra, namely the adroit and persistent application of categorical methods.
9. He also studies linkage theory, Rees algebras, homological theory of modules over Noetherian rings, local cohomology, symbolic powers of ideals, Cohen-Macaulay rings, Gorenstein rings and Hilbert-Kunz functions.
10. His results on Fourier-Mukai transforms solve many problems within algebraic geometry, and have been influential in homological and commutative algebra, orbifold and quantum cohomology, minimal model program, classification of Fano varieties, moduli constructions, representation theory and combinatorics.