http://dspace.nbuv.gov.ua:80/handle/123456789/150408 2026-04-20T06:21:52Z http://dspace.nbuv.gov.ua:80/handle/123456789/188428 Representations of ordered doppelsemigroups by binary relations Zhuchok, Y.V.; Koppitz, J. We extend the study of doppelsemigroups and introduce the notion of an ordered doppelsemigroup. We construct the ordered doppelsemigroup of binary relations on an arbitrary set and prove that every ordered doppelsemigroup is isomorphic to some ordered doppelsemigroup of binary relations. In particular, we obtain an analogue of Cayley’s theorem for semigroups in the class of doppelsemigroups. We also describe the representations of ordered doppelsemigroups by binary transitive relations. 2019-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/188427 Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring II, Quasilocal Case Visweswaran, S.; Vadhel, P. The rings we consider in this article are commutative with identity 1 ≠ 0 and are not fields. Let R be a ring. We denote the collection of all proper ideals of R by I(R) and the collection I(R) \ {(0)} by I(R)*. Let H(R) be the graph associated with R whose vertex set is I(R)* and distinct vertices I, J are adjacent if and only if IJ ≠ (0). The aim of this article is to discuss the planarity of H(R) in the case when R is quasilocal. 2019-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/188426 On certain families of sparse numerical semigroups with Frobenius number even Tizziotti, G.; Villanueva, J. This paper is about sparse numerical semigroups and applications in the Weierstrass semigroups theory. We describe and find the genus of certain families of sparse numerical semigroups with Frobenius number even and we also study the realization of the elements on these families as Weierstrass semigroups. 2019-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/188425 A Ramsey algebraic study of matrices Teoh, Z.Y.; Teh, W.C. The notion of a topological Ramsey space was introduced by Carlson some 30 years ago. Studying the topological Ramsey space of variable words, Carlson was able to derive many classical combinatorial results in a unifying manner. For the class of spaces generated by algebras, Carlson had suggested that one should attempt a purely combinatorial approach to the study. This approach was later formulated and named Ramsey algebra. In this paper, we continue to look at heterogeneous Ramsey algebras, mainly characterizing various Ramsey algebras involving matrices. 2019-01-01T00:00:00Z