ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

Discussiones Mathematicae - General Algebra and Applications

Cite Score (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications


Discussiones Mathematicae General Algebra and Applications 24(1) (2004) 95-114


Stephan Foldes

Institute of Mathematics
Tampere University of Technology
33101 Tampere, Finland


Sándor Radeleczki

Institute of Mathematics
University of Miskolc
3515 Miskolc-Egyetemváros, Hungary



Intervals in binary or n-ary relations or other discrete structures generalize the concept of interval in an ordered set. They are defined abstractly as closed sets of a closure system on a set V, satisfying certain axioms. Decompositions are partitions of V whose blocks are intervals, and they form an algebraic semimodular lattice. Lattice-theoretical properties of decompositions are explored, and connections with particular types of intervals are established.

Keywords: interval, closure system, modular decomposition, semimodular lattice, partition lattice, strong set, lexicographic sum.

2000 Mathematics Subject Classification: Primary 06B05, 06A15, 06C10, 08A02; Secondary 05C99, 03C99.


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Received 26 November 2003
Revised 13 June 2004