http://dspace.nbuv.gov.ua:80/handle/123456789/150373 2026-04-20T14:27:34Z 2026-04-20T14:27:34Z http://dspace.nbuv.gov.ua:80/handle/123456789/158440 2019-09-01T22:25:24Z 2012-01-01T00:00:00Z

To the 100th anniversary of the birth of Sergei Nikolaevich Chernikov On May 11, 2012, we celebrate the 100th anniversary of the birth of Sergei Nikolaevich Chernikov (1912 – 1987), a great mathematician, one of the main founders of infinite group theory.

2012-01-01T00:00:00Z Shevrin, L.N. http://dspace.nbuv.gov.ua:80/handle/123456789/152212 2019-06-08T22:25:21Z 2012-01-01T00:00:00Z

Semigroups with certain finiteness conditions and Chernikov groups Shevrin, L.N. The main purpose of this short survey is to show how groups of special structure, which are accepted to be called Chernikov groups, appeared in the considerations of semigroups with certain finiteness conditions. A structure of groups with several such conditions has been described (they turned out to be special types of Chernikov groups). Lastly, a question concerning some special type of Chernikov groups is recalled; this question was raised by the author more than 35 years ago, and it is still open.

2012-01-01T00:00:00Z Selkin, V. http://dspace.nbuv.gov.ua:80/handle/123456789/152211 2019-06-08T22:25:19Z 2012-01-01T00:00:00Z

On factorizations of limited solubly ω-saturated formations Selkin, V. If F = F₁…Ft is the product of the formations F₁,…,Ft and F ≠ F₁…Fi−₁Fi+₁…Ft for all i = 1,…,t, then we call this product a non-cancellative factorization of the formation F. In this paper we gives a description of factorizable limited solubly ω-saturated formations.

2012-01-01T00:00:00Z Kashu, A.I. http://dspace.nbuv.gov.ua:80/handle/123456789/152210 2019-06-08T22:25:20Z 2012-01-01T00:00:00Z

On inverse operations in the lattices of submodules Kashu, A.I. In the lattice L(RM) of submodules of an arbitrary left R-module RM four operation were introduced and investigated in the paper [3]. In the present work the approximations of inverse operations for two of these operations (for α-product and ω-coproduct) are defined and studied. Some properties of left quotient with respect to α-product and right quotient with respect to ω-coproduct are shown, as well as their relations with the lattice operations in L(RM) (sum and intersection of submodules). The particular case RM = RR of the lattice L(RR) of left ideals of the ring R is specified.

2012-01-01T00:00:00Z