Hyperbolic geometry in terms of point-reflections or of line-orthogonality.
Pambuccian, Victor (2004)
Mathematica Pannonica
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Displaying similar documents to “Reflection loops of spaces with congruence and hyperbolic incidence structure”
Hyperbolic geometry in terms of point-reflections or of line-orthogonality.
Lexicographic product decompositions of half linearly ordered loops
Milan Demko (2007)
Czechoslovak Mathematical Journal
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In this paper we prove for an hl-loop an assertion analogous to the result of Jakubík concerning lexicographic products of half linearly ordered groups. We found conditions under which any two lexicographic product decompositions of an hl-loop with a finite number of lexicographic factors have isomorphic refinements.
On the planarity of the equilateral, isogonal pentagon.
Pambuccian, Victor (2003)
Mathematica Pannonica
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Direct product decompositions of directed groups
Ján Jakubík (1989)
Czechoslovak Mathematical Journal
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On some hyperbolic planes from finite projective planes.
Celik, Basri (2001)
International Journal of Mathematics and Mathematical Sciences
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On congruences and ideals of partially ordered quasigroups
Milan Demko (2008)
Czechoslovak Mathematical Journal
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Some results concerning congruence relations on partially ordered quasigroups (especially, Riesz quasigroups) and ideals of partially ordered loops are presented. These results generalize the assertions which were proved by Fuchs in [5] for partially ordered groups and Riesz groups.
Tarski Geometry Axioms – Part II
Roland Coghetto, Adam Grabowski (2016)
Formalized Mathematics
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In our earlier article [12], the first part of axioms of geometry proposed by Alfred Tarski [14] was formally introduced by means of Mizar proof assistant [9]. We defined a structure TarskiPlane with the following predicates: of betweenness between (a ternary relation), of congruence of segments equiv (quarternary relation), which satisfy the following properties: congruence symmetry (A1), congruence equivalence relation (A2), congruence identity (A3), segment construction (A4), SAS...