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, ...

In the paper we investigate algebras and logics defined for classes of partial quasiary predicates. Informally speaking, such predicates are partial predicates defined over partial states (partial assignments) of ...

Pension provision is an element of the pension system that ensures sustainable socio-economic development of the state as a whole. The article discusses the current problems of the pension system in Ukraine, ways to overcome ...

The article analyzes the directions for Ukrainian economic recovery after the war. The successes stories of the countries, that restored their economies after the war, were explored. As a result the best practices of Israel ...