http://dspace.nbuv.gov.ua:80/handle/123456789/150361 2026-04-18T10:28:03Z http://dspace.nbuv.gov.ua:80/handle/123456789/154882 On separable group rings Szeto, G.; Lianyong Xue Let G be a finite non-abelian group, R a ring with 1, and Ĝ the inner automorphism group of the group ring RG over R induced by the elements of G. Then three main results are shown for the separable group ring RG over R: (i) RG is not a Galois extension of (RG)Ĝ with Galois group Ĝ when the order of G is invertible in R, (ii) an equivalent condition for the Galois map from the subgroups H of G to (RG)H by the conjugate action of elements in H on RG is given to be one-to-one and for a separable subalgebra of RG having a preimage, respectively, and (iii) the Galois map is not an onto map. Remove selected 2010-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/154875 Groups of linear automata Oliynyk, A. The scalar automata as a special class of groups of linear automata over modules are introduced. The groups of scalar automata are classified. 2010-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/154874 Preradicals and submodules Maturin, Y. Some collections of submodules of a module defined by certain conditions are studied. 2010-01-01T00:00:00Z 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