2 citations · 2 across the 6 of their papers we have counts for
9 papers
The Cayley graph of a quandle
David Dolžan, Bogdana Oliynyk
In this paper, we investigate structural properties of the Cayley graph of a quandle and describe this graph for several important classes of quandles, including conjugation, Takas…
The unitary Cayley graph of upper triangular matrix rings
Waldemar Hołubowski, Sergiy Kozerenko, Bogdana Oliynyk +1
The unitary Cayley graph of a finite unital ring is the simple graph with vertex set in which two elements and are connected by an edge if and only if i…
Locally standard measure algebras
Oksana Bezushchak, Bogdana Oliynyk
We parameterize countable locally standard measure algebras by pairs of a Steinitz number and a real number greater or equal to 1. This is an analog of the theorems of J.Dixmier an…
Ideals of general linear Lie algebras of infinite-dimensional vector spaces
Oksana Bezushchak, Waldemar Hołubowski, Bogdana Oliynyk
Let V be an infinite-dimensional vector space over a field of characteristic not equal to 2. We classify ideals of the Lie algebra gl(V) of all linear transformations of the space…
A note on the triameter of graphs
Artem Hak, Sergiy Kozerenko, Bogdana Oliynyk
In this note, we give answers to three questions from the paper [A. Das, Triameter of graphs, Discuss. Math. Graph Theory, 41 (2021), 601--616]. Namely, we obtain a tight lower bou…
Hamming spaces and locally matrix algebras
Oksana Bezushchak, Bogdana Oliynyk
We introduce an abstract definition of a Hamming space that generalizes standard Hamming spaces . We classify countable locally standard Hamming spa…
Morita equivalent unital locally matrix algebras
Oksana Bezushchak, Bogdana Oliynyk
We describe Morita equivalence of unital locally matrix algebras in terms of their Steinitz parametrization. Two countable dimensional unital locally matrix algebras are Morita equ…
On primary decompositions of unital locally matrix algebras
Oksana Bezushchak, Bogdana Oliynyk
We construct a unital locally matrix algebra of uncountable dimension that (1) does not admit a primary decomposition, (2) has an infinite locally finite Steinitz number. It gives…
Unital locally matrix algebras and Steinitz numbers
Oksana Bezushchak, Bogdana Oliynyk
An -algebra with unit is said to be a locally matrix algebra if an arbitrary finite collection of elements from lies in a subalgebra wit…