Tolerances on posets
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Publication:6064729
DOI10.18514/MMN.2023.4033arXiv2112.05580OpenAlexW4385169411MaRDI QIDQ6064729
Publication date: 12 December 2023
Published in: Miskolc Mathematical Notes (Search for Journal in Brave)
Abstract: The concept of a tolerance relation, shortly called tolerance, was studied on various algebras since the seventieth of the twentieth century by B. Zelinka and the first author. 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 showed that lattices can be factorized by means of tolerances in a natural way, and J. Grygiel and S. Radelecki 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.
Full work available at URL: https://arxiv.org/abs/2112.05580
posetblockconvextolerance relationdirectedIsomorphism Theoremcongruence on a posetquotient poset by a tolerancerelatively complemented poset
Partial orders, general (06A06) Structure theory of algebraic structures (08A05) Algebraic aspects of posets (06A11) Relational systems, laws of composition (08A02)
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