http://dspace.nbuv.gov.ua:80/handle/123456789/150370 2026-04-20T14:44:06Z http://dspace.nbuv.gov.ua:80/handle/123456789/154868 Quasi-duo Partial skew polynomial rings Cortes, W.; Ferrero, M.; Gobbi, L. In this paper we consider rings R with a partial action α of Z on R. We give necessary and sufficient conditions for partial skew polynomial rings and partial skew Laurent polynomial rings to be quasi-duo rings and in this case we describe the Jacobson radical. Moreover, we give some examples to show that our results are not an easy generalization of the global case. 2011-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/154866 On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point Chuchman, I. In this paper we study the semigroup IC(I,[a]) (IO(I,[a])) of closed (open) connected partial homeomorphisms of the unit interval I with a fixed point a∈I. We describe left and right ideals of IC(I,[0]) and the Green's relations on IC(I,[0]). We show that the semigroup IC(I,[0]) is bisimple and every non-trivial congruence on IC(I,[0]) is a group congruence. Also we prove that the semigroup IC(I,[0]) is isomorphic to the semigroup IO(I,[0]) and describe the structure of a semigroup II(I,[0])=IC(I,[0])⊔IO(I,[0]). As a corollary we get structures of semigroups IC(I,[a]) and IO(I,[a]) for an interior point a∈I. 2011-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/154863 Minimax isomorphism algorithm and primitive posets Bondarenko, V.M. The notion of minimax equivalence of posets, and a close notion of minimax isomorphism, introduced by the author are widely used in the study of quadratic Tits forms (in particular, for the description of P-critical and P-supercritical posets). In this paper, for an important special case, we modify an algorithm of classifying all posets minimax isomorphic to a given one (described earlier by the author together with M.V.Stepochkina) by introducing the concept of weak isomorphism. 2011-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/154862 On Pseudo-valuation rings and their extensions Bhat, V.K. Let R be a commutative Noetherian Q-algebra (Q is the field of rational numbers). Let σ be an automorphism of R and δ a σ-derivation of R. We define a δ-divided ring and prove the following: (1)If R is a pseudo-valuation ring such that x∉P for any prime ideal P of R[x;σ,δ], and P∩R is a prime ideal of R with σ(P∩R)=P∩R and δ(P∩R)⊆P∩R, then R[x;σ,δ] is also a pseudo-valuation ring. (2)If R is a δ-divided ring such that x∉P for any prime ideal P of R[x;σ,δ], and P∩R is a prime ideal of R with σ(P∩R)=P∩R and δ(P∩R)⊆P∩R, then R[x;σ,δ] is also a δ-divided ring. 2011-01-01T00:00:00Z