10 papers · 1 filter
On the Structure of Low-Dimensional Poisson Algebras over Arbitrary Fields
A. V. Petrov, O. O. Pypka
We investigate the structure of Poisson algebras of dimensions at most three over an arbitrary field. Our approach is based on the internal structure of the associated commutative…
Dedekind Poisson Algebras over Arbitrary Fields
A. I. Plakosh, O. O. Pypka
We study Poisson algebras in which every Poisson subalgebra is a Poisson ideal, called Dedekind Poisson algebras, over arbitrary fields and without any finite-dimensionality assump…
Leibniz rings: some basic and structural results
L. A. Kurdachenko, O. O. Pypka, M. M. Semko
In this paper, we study the fundamental properties of Leibniz rings. Special attention is given to the structure of Leibniz rings whose additive group is "small". The results obtai…
Some three-dimensional non-nilpotent Leibniz algebras: automorphism groups
Leonid A. Kurdachenko, Oleksandr O. Pypka, Igor Ya. Subbotin
The article presents the structure of the automorphism groups of two types of non-nilpotent Leibniz algebras with a dimension of 3.
On some relationships between the center and the derived subalgebra in Poisson (2-3)-algebras
P. Ye. Minaiev, O. O. Pypka, I. V. Shyshenko
One of the classic results of group theory is the so-called Schur theorem. It states that if the central factor-group of a group is finite, then its derived subgroup $…
On some relationships between the centers and the derived ideal in Leibniz 3-algebras
P. Ye. Minaiev, O. O. Pypka
One of the classic results of group theory is the so-called Schur theorem. It states that if the central factor-group of a group is finite, then its derived subgroup $…