E104-01 - Forschungsbereich Algebra E104 - Institut für Diskrete Mathematik und Geometrie
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Journal:
MISKOLC MATHEMATICAL NOTES
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ISSN:
1787-2405
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Date (published):
2023
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Number of Pages:
12
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Publisher:
UNIV MISKOLC INST MATH
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Peer reviewed:
Yes
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Keywords:
poset; tolerance relation; congruence on a poset; block; directed; convex; relatively complemented poset; quotient poset by a tolerance; Isomorphism Theorem
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Abstract:
The concept of a tolerance relation, shortly called tolerance, was studied on various algebras since the seventies of the twentieth century by B. Zelinka and the first author (see e.g. [6] and the monograph [1] and the references therein). Since tolerances need not be transitive, their blocks may overlap and hence in general the set of all blocks of a tolerance cannot be converted into a quotient algebra in the same way as in the case of congruences. However, G. Cz´edli ([7]) showed that lattices can be factorized by means of tolerances in a natural way, and J. Grygiel and S. Radeleczki ([8]) proved some variant of an Isomorphism Theorem for tolerances on lattices. The aim of the present paper is to extend the concept of a tolerance on a lattice to posets in such a way that results similar to those obtained for tolerances on lattices can be derived.
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Project (external):
Austrian Science Fund Czech Science Foundation IGA
