In this note we investigate the structure of contact Lie algebras when the ground field is of characteristic 2. In order to describe the simple constituent of contact Lie algebras, by using computer algebra system, GAP, ...

The definition of a resolvent, introduced in the paper mentioned in the title, is simplified, and some misprints in that paper are corrected.

The notion of a topological Ramsey space was introduced by Carlson some 30 years ago. Studying the topological Ramsey space of variable words, Carlson was able to derive many classical combinatorial results in a unifying ...

Let G be a group and p a prime number. G is said to be a Yp-group if whenever K is a p-subgroup of G then every subgroup of K is an S-permutable subgroup in NG(K). The group G is a soluble PST-group if and only if G is ...

Let S = K[x1, x2, . . . , xn] be a standard graded K-algebra for any field K. Without using any heavy tools of com- mutative algebra we compute the Hilbert series of graded S-module S/I, where I is a monomial ideal.

Some properties of abnormal subgroups in generalized soluble groups are considered. In particular, the transitivity of abnormality in metahypercentral groups is proven. Also it is proven that a subgroup H of a radical ...

Let R and R′ be alternative rings. In this article we investigate the additivity of surjective elementary maps of R × R′ . As a main theorem, we prove that if R contains a non-trivial idempotent satisfying some conditions, ...

The article analyzes the definitions of the concepts “aggression” and “genocide” as types of armed violence presented in Ukrainian and world political science. The definitions of these concepts reflected in international ...

We show that the main result of algebraic Morse theory can be obtained as a consequence of the perturbation lemma of Brown and Gugenheim.