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Abstract complexes, their homologies and applications
Authors: Cataranciuc Sergiu, Soltan Petru
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Abstract
The complex of multi-ary relations Kn is defined in a more natural way than it was defined in [18, 58, 59]. The groups of homologies and co-homologies of this complex over the group of integer numbers are constructed. The methods used for these constructions are for the most part analogous with classical methods [2, 32, 52], but sometimes they are based on methods from [18, 44, 58]. The importance and originality consist in application of the multi-ary relations of a set of objects in construction of\ homologies. This allows to extend areas of theoretical researches and non-trivial practical applications in a lot of directions. Other abstract structures, which are developed in a natural way from generalized complex of multi-ary relations are also examined. New notions such as the notions of abstract quasi-simplex and its homologies, the complex of abstract simplexes and the complex of the n-dimensional abstract cubes are introduced.E-mail: ,
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Contents
- Properties of final unrefinable chains of groups topologies
- On subsemimodules of semimodules
- Abstract complexes, their homologies and applications
- A criterion for parametrical completeness in the 8-valued algebraic model of modal logic S5
- On Solvability of one Class of Hammerstein Nonlinear Integral Equations
- Algorithms for Determining the Transient and Differential Matrices in Finite Markov Processes
- On the centralizers of finite subgroups in quasi-HNN groups
- New Inequalities of Hardy-Hilbert Type
- On the Diophantine equation xxyyk(y)=zzp
