Algebra and Discrete Mathematics, 2004, Vol. 3 http://dspace.nbuv.gov.ua:80/handle/123456789/150330 2026-04-22T13:01:15Z 2026-04-22T13:01:15Z Correct classes of modules Wisbauer, R. http://dspace.nbuv.gov.ua:80/handle/123456789/156603 2019-06-18T22:26:51Z 2004-01-01T00:00:00Z Correct classes of modules Wisbauer, R. For a ring R, call a class C of R-modules (pure-) mono-correct if for any M, N ∈ C the existence of (pure) monomorphisms M → N and N → M implies M ≃ N. Extending results and ideas of Rososhek from rings to modules, it is shown that, for an R-module M, the class σ[M] of all M-subgenerated modules is mono-correct if and only if M is semisimple, and the class of all weakly M-injective modules is mono-correct if and only if M is locally noetherian. Applying this to the functor ring of R-Mod provides a new proof that R is left pure semisimple if and only if R-Mod is pure-mono-correct. Furthermore, the class of pure-injective Rmodules is always pure-mono-correct, and it is mono-correct if and only if R is von Neumann regular. The dual notion epi-correctness is also considered and it is shown that a ring R is left perfect if and only if the class of all flat R-modules is epi-correct. At the end some open problems are stated. 2004-01-01T00:00:00Z Subsets of defect 3 in elementary Abelian 2-groups Novikov, B.V. Polyakova, L.Yu. http://dspace.nbuv.gov.ua:80/handle/123456789/156602 2019-06-18T22:25:42Z 2004-01-01T00:00:00Z Subsets of defect 3 in elementary Abelian 2-groups Novikov, B.V.; Polyakova, L.Yu. 2004-01-01T00:00:00Z On simple groups of large exponents Sonkin, D. http://dspace.nbuv.gov.ua:80/handle/123456789/156601 2019-06-18T22:26:21Z 2004-01-01T00:00:00Z On simple groups of large exponents Sonkin, D. It is shown that the set of pairwise non-isomorphic 2-generated simple groups of exponent n (n ≥ 2⁴⁸ and n is odd or divisible by 2⁹ ) is of cardinality continuum. As a corollary, for any sufficiently large n the set of pairwise non-isomorphic 2-generated groups of exponent n is of cardinality continuum. 2004-01-01T00:00:00Z On intersections of normal subgroups in groups Kulikova, O.V. http://dspace.nbuv.gov.ua:80/handle/123456789/156599 2019-06-18T22:28:42Z 2004-01-01T00:00:00Z On intersections of normal subgroups in groups Kulikova, O.V. The paper is a generalization of [2]. For a group H = ‹A|O›, conditions for the equality Ñ₁ ∩ Ñ₂ = Ñ₁, Ñ₂] are given in terms of pictures, where Ñi is the normal closure of a set R¯ i ⊂ H for i = 1, 2. 2004-01-01T00:00:00Z