2019
Том 71
№ 11

All Issues

Petrenko B. V.

Articles: 2
Brief Communications (Ukrainian)

On complementability of certain generalized hypercenters in Artinian modules

Kurdachenko L. A., Petrenko B. V., Subbotin I. Ya.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 11. - pp. 1548–1552

We prove that, in an Artinian module, the upper FC-hypercenter over an infinite FC-hypercentral locally solvable group has a direct complement. Thus, we obtain a generalization of one of Zaitsev’s theorems and one of Duan’s theorems.

Article (Ukrainian)

On direct decompositions in modules over group rings

Petrenko B. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 2. - pp. 255–261

In the theory of infinite groups, one of the most important useful generalizations of the classical Maschke theorem is the Kovačs-Newman theorem, which establishes sufficient conditions for the existence of G-invariant complements in modules over a periodic group G finite over the center. We genralize the Kovačs-Newman theorem to the case of modules over a group ring KG, where K is a Dedekind domain.