Algebra and Discrete Mathematics, 2019, Vol. 28, № 1 http://dspace.nbuv.gov.ua:80/handle/123456789/188466 2026-04-22T10:05:44Z 2026-04-22T10:05:44Z Some combinatorial characteristics of closure operations Nguyen Hoang Son Vu Duc Thi http://dspace.nbuv.gov.ua:80/handle/123456789/188483 2023-03-02T23:27:06Z 2019-01-01T00:00:00Z Some combinatorial characteristics of closure operations Nguyen Hoang Son; Vu Duc Thi The aim of this paper investigates some combinatorial characteristics of minimal key and antikey of closure operations. We also give effective algorithms finding minimal keys and antikeys of closure operations. We estimate these algorithms. Some remarks on the closeness of closure operations class under the union and direct product operations are also studied in this paper. 2019-01-01T00:00:00Z Representations of strongly algebraically closed algebras Molkhasi, A. Shum, K.P. http://dspace.nbuv.gov.ua:80/handle/123456789/188482 2023-03-03T23:27:18Z 2019-01-01T00:00:00Z Representations of strongly algebraically closed algebras Molkhasi, A.; Shum, K.P. We introduce the notion of q′-compactness for MV-algebras. One of the main results of the paper is a characterization of a class of orthomodular lattices that are horizontal sums of strongly algebraically closed algebras. 2019-01-01T00:00:00Z Lie algebras of derivations with large abelian ideals Klymenko, I.S. Lysenko, S.V. Petravchuk, A. http://dspace.nbuv.gov.ua:80/handle/123456789/188481 2023-03-02T23:27:15Z 2019-01-01T00:00:00Z Lie algebras of derivations with large abelian ideals Klymenko, I.S.; Lysenko, S.V.; Petravchuk, A. We study subalgebras L of rank m over R of the Lie algebra Wn(K) with an abelian ideal I ⊂ L of the same rank m over R. 2019-01-01T00:00:00Z On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs Inpoonjai, P. Jiarasuksakun, T. http://dspace.nbuv.gov.ua:80/handle/123456789/188480 2023-03-02T23:27:13Z 2019-01-01T00:00:00Z On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs Inpoonjai, P.; Jiarasuksakun, T. Magic rectangles are a classical generalization of the well-known magic squares, and they are related to graphs. A graph G is called degree-magic if there exists a labelling of the edges by integers 1, 2, . . . , |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal to (1 + |E(G)|) deg(v)/2. Degree-magic graphs extend supermagic regular graphs. In this paper, we present a general proof of the necessary and sufficient conditions for the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs. We apply this existence to construct supermagic regular graphs and to identify the sufficient condition for even n-tuple magic rectangles to exist. 2019-01-01T00:00:00Z