Algebra and Discrete Mathematics, 2010, Vol. 10, № 1 http://dspace.nbuv.gov.ua:80/handle/123456789/150364 2026-04-18T13:16:25Z 2026-04-18T13:16:25Z On separable group rings Szeto, G. Lianyong Xue http://dspace.nbuv.gov.ua:80/handle/123456789/154882 2019-06-16T22:31:29Z 2010-01-01T00:00:00Z 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 Groups of linear automata Oliynyk, A. http://dspace.nbuv.gov.ua:80/handle/123456789/154875 2019-06-16T22:31:51Z 2010-01-01T00:00:00Z 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 Preradicals and submodules Maturin, Y. http://dspace.nbuv.gov.ua:80/handle/123456789/154874 2019-06-16T22:31:51Z 2010-01-01T00:00:00Z Preradicals and submodules Maturin, Y. Some collections of submodules of a module defined by certain conditions are studied. 2010-01-01T00:00:00Z Projectivity and flatness over the graded ring of semi-coinvariants Guedenon, T. http://dspace.nbuv.gov.ua:80/handle/123456789/154619 2019-06-15T22:31:54Z 2010-01-01T00:00:00Z Projectivity and flatness over the graded ring of semi-coinvariants Guedenon, T. Let k be a field, C a bialgebra with bijective antipode, A a right C-comodule algebra, G any subgroup of the monoid of grouplike elements of C. We give necessary and sufficient conditions for the projectivity and flatness over the graded ring of semi-coinvariants of A. When A and C are commutative and G is any subgroup of the monoid of grouplike elements of the coring A⊗C, we prove similar results for the graded ring of conormalizing elements of A. 2010-01-01T00:00:00Z