4 citations · 7 across the 7 of their papers we have counts for
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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…