Rezümékötet 2008. - vmtdk

É L E T T E L E N T E R M É S Z E T T U D O M Á N Y O K
É S M Û S Z A K I T U D O M Á N Y O K
ON A CLASS OF HOMOMORPHISM-HOMOGENOUS
SEMILINEAR SPACES
Author: Éva JUNGÁBEL 4 th year student
Supervisor: Dr Dragan MAŠULOVIÆ university professor, Dr Igor DOLINKA university professor
Institution: University of Novi Sad, Faculty of Science, Department of Mathematics and Informatics, Novi Sad
Hungarian college for higher education in Vojvodina
This paper discusses one class of homomorphism-homogenous semilinear spaces.
A stucture S is homomorphism-homogeneous if every homomorphism from S’ to S’’, where S’ and S’’ are two finitely
induced substructures, can be extended to an endomorphism of S.
A semilinear space is a non-empty finite set of points, together with a collectoin of subsets called lines such that
every line contains at least two points and any pair of points is contained in at most one line. A line which contains
more than two points is referred to as a regular line. A line wich contains exactly two points is called singular. Homomorphism-homogenous
semilinear spaces containing two regular intersecting lines have been described. In order to complete
to characterization of homomorphism-homogeneous semilinear spaces it is necessary to describe homomorphismhomogenous
semilinear spaces where regular lines are disjoint. This paper considers finite semilinear spaces which
fulfill the following two conditions: There are exactly two regular lines a and b, which are disjoint, and every point belongs
to either the line a or the line b. We distinguish several cases according to the structure of singular lines and we
give a complete characterisation for each case. The main result of this paper is a theorem which states that an above
described semilinear space is homomorphism-homogenous if and only if it belongs to one of the following classes:
Keywords: semilinear spaces, homomorphism-homogeneity
N Y O S D I Á K K Ö R I K O N F E R E N C I A
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