2019
Том 71
№ 11

# Zainalov B. R.

Articles: 3
Article (Russian)

### First nontrivial group of homologies of simplicial schemes of unimodular frames over the Dedekind ring

Ukr. Mat. Zh. - 2018. - 70, № 9. - pp. 1231-1248

We prove a theorem on generation of the first nontrivial group of homologies of a simplicial scheme of unimodular frames over the Dedekind ring by standard cycles.

Article (Russian)

### Preacyclicity over the rings with infinite fields of residues

Ukr. Mat. Zh. - 2016. - 68, № 2. - pp. 202-216

We consider a simplicial scheme, its geometric realization, and the required properties of the simplicial scheme of unimodal frames and prove both a sufficiently strong theorem on acyclicity for the simplicial scheme of unimodal frames and a theorem stating that the first nontrivial group of homologies is generated by standard cycles over the rings with infinite fields of residues.

Article (Russian)

### Homological stabilization for dedekind rings of the arithmetic type

Ukr. Mat. Zh. - 2012. - 64, № 11. - pp. 1464-1476

We study the problem of stabilization in the higher $K$ -theory of rings and improved stabilization. The triviality of the group of standard cycles is established in the case of arithmetic-type rings. Some applications of the obtained results to the problem of homological stabilization are presented.