http://dspace.nbuv.gov.ua:80/handle/123456789/150365 2026-04-18T10:28:03Z http://dspace.nbuv.gov.ua:80/handle/123456789/154873 Symbolic Rees algebras, vertex covers and irreducible representations of Rees cones Dupont, L.D.; Villarreal, R.H. Let G be a simple graph and let Ic(G) be its ideal of vertex covers. We give a graph theoretical description of the irreducible b-vertex covers of G, i.e., we describe the minimal generators of the symbolic Rees algebra of Ic(G). Then we study the irreducible b-vertex covers of the blocker of G, i.e., we study the minimal generators of the symbolic Rees algebra of the edge ideal of G. We give a graph theoretical description of the irreducible binary b-vertex covers of the blocker of G. It is shown that they correspond to irreducible induced subgraphs of G. As a byproduct we obtain a method, using Hilbert bases, to obtain all irreducible induced subgraphs of G. In particular we obtain all odd holes and antiholes. We study irreducible graphs and give a method to construct irreducible b-vertex covers of the blocker of G with high degree relative to the number of vertices of G. 2010-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/154872 On τ-closed n-multiply ω-composition formations with Boolean sublattices Zhiznevsky, P. In the universe of finite groups the description of τ-closed n-multiply ω-composition formations with Boolean sublattices of τ-closed n-multiply ω-composition subformations is obtained. 2010-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/154871 Steadiness of polynomial rings Zemlicka, J. A module M is said to be small if the functor Hom(M,−) commutes with direct sums and right steady rings are exactly those rings whose small modules are necessary finitely generated. We give several results on steadiness of polynomial rings, namely we prove that polynomials over a right perfect ring such that EndR(S) is finitely generated over its center for every simple module S form a right steady ring iff the set of variables is countable. Moreover, every polynomial ring in uncountably many variables is non-steady. 2010-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/154870 On separable and H-separable polynomials in skew polynomial rings of several variables Ikehata, S. Let B be a ring with 1, and {ρ1,⋯,ρe} a set of automorphisms of B. Let B[X1,⋯,Xe;ρ1,⋯,ρe;{uij}] be the skew polynomial ring of automorphism type. In this paper, we shall give equivalent conditions that the residue ring of B[X1,⋯,Xe;ρ1,⋯,ρe;{uij}] by the ideal generated by a set {Xm11−u1,⋯,Xmee−ue} to be separable or H-separable over B. 2010-01-01T00:00:00Z