We extend the classical theory of factorization in noncommutative integral domains to the more general classes of right saturated rings and right cyclically complete rings. Our attention is focused, in particular, on the ...

The famous Ukrainian mathematician and educator, Doctor of Physical and Mathematical Sciences, Professor Fedir Mykolayovych Lyman passed away on June 13, 2020 after a long illness.

In this paper, we introduce filtered and graded Procesi extensions of filtered and graded rings as a natural modification of Procesi extensions of rings. We show that these extensions behave well from the geometric point of view.

It is shown that for groups G and H that act faithfully by finite state automorphisms on regular rooted trees their free product G∗H admits a faithful action by finite state automorphisms on some regular rooted tree.

Representations of finite groups as automata groups over a binary alphabet are investigated. The subclass of groups of automata with no cycles with exit is studied.

A Schmidt group is a non-nilpotent group in which every proper subgroup is nilpotent. A subgroup A of a group G is semi-normal in G if there exists a subgroup B of G such that G = AB and AB1 is a proper subgroup of G for ...

In this paper the metacyclic Miller-Moreno p-groups which appear as the additive groups of finite local nearrings are classified.

In this article, we give two examples of finitely presented quadratic algebras (algebras presented by quadratic relations) of intermediate growth.

Phantom homology arises in tight closure theory due to small non-exactness when `kernel' is not equal to `image' but `kernel' is in the tight closure of the `image'. In this paper we study a typical flat extension, which ...

Some collections of submodules of a module defined by certain conditions are studied. A generalization of the notion of radical (preradical) filter is considered. We study the form of filters of semisimple modules and direct sums.