4 citations · 7 across the 7 of their papers we have counts for
8 papers
Dimension subrings of Lie rings
Vasily Ionin, Roman Mikhailov, Tima Petrov
We show that, unlike the lower central series, the dimension series of a Lie ring need not stabilize when two consecutive terms coincide; in fact, arbitrarily long finite plateaux…
Dimension quotients as boundary limits: the general case
Roman Mikhailov
We identify, functorially, the boundary limit of a simply defined presentation functor with the dimension quotient, both for groups and for Lie rings over integers.
The Parafree Conjecture for associative algebras
Vasily Ionin, Roman Mikhailov
For every base field, we construct a finitely generated parafree augmented associative algebra with countably infinite-dimensional second homology. This disproves the analogue of t…
Two results on asphericity
Roman Mikhailov
We construct an explicit finite chain of non-aspherical group presentation complexes in which is Cockcroft…
Dimension quotients as boundary limits
Roman Mikhailov
For a functor from the category of free presentations of a group to the category of all groups we define the boundary limit as an image of the natural map from limit to colimit. We…
Homotopy groups as centers of finitely presented groups
Roman Mikhailov, Jie Wu
For every finite abelian group and , we construct a finitely presented group defined by explicit generators and relations, such that its center is .