Semimodularity in lower continuous strongly dually atomic lattices

Andrzej Walendziak

Archivum Mathematicum (1996)

  • Volume: 032, Issue: 3, page 163-165
  • ISSN: 0044-8753

Abstract

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For lattices of finite length there are many characterizations of semimodularity (see, for instance, Grätzer [3] and Stern [6]–[8]). The present paper deals with some conditions characterizing semimodularity in lower continuous strongly dually atomic lattices. We give here a generalization of results of paper [7].

How to cite

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Walendziak, Andrzej. "Semimodularity in lower continuous strongly dually atomic lattices." Archivum Mathematicum 032.3 (1996): 163-165. <http://eudml.org/doc/247859>.

@article{Walendziak1996,
abstract = {For lattices of finite length there are many characterizations of semimodularity (see, for instance, Grätzer [3] and Stern [6]–[8]). The present paper deals with some conditions characterizing semimodularity in lower continuous strongly dually atomic lattices. We give here a generalization of results of paper [7].},
author = {Walendziak, Andrzej},
journal = {Archivum Mathematicum},
keywords = {lower continuous lattices; strongly dually atomic lattices; semimodular and atomic lattices; lower continuous lattices; strongly dually atomic lattices; semimodular lattices},
language = {eng},
number = {3},
pages = {163-165},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Semimodularity in lower continuous strongly dually atomic lattices},
url = {http://eudml.org/doc/247859},
volume = {032},
year = {1996},
}

TY - JOUR
AU - Walendziak, Andrzej
TI - Semimodularity in lower continuous strongly dually atomic lattices
JO - Archivum Mathematicum
PY - 1996
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 032
IS - 3
SP - 163
EP - 165
AB - For lattices of finite length there are many characterizations of semimodularity (see, for instance, Grätzer [3] and Stern [6]–[8]). The present paper deals with some conditions characterizing semimodularity in lower continuous strongly dually atomic lattices. We give here a generalization of results of paper [7].
LA - eng
KW - lower continuous lattices; strongly dually atomic lattices; semimodular and atomic lattices; lower continuous lattices; strongly dually atomic lattices; semimodular lattices
UR - http://eudml.org/doc/247859
ER -

References

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  1. Lattice Theory, 3rd edition, American Mathematical Society, Providence, RI, 1967. Zbl0537.06001MR0227053
  2. Algebraic Theory of Lattices, Prentice-Hall, Englewood Cliffs (N.J.), 1973. 
  3. General Lattice Theory, Birhäuser Basel, 1978. MR0509213
  4. The Kuroš-Ore Theorem, finite and infinite decompositions, Studia Sci. Math. Hungar., 17(1982), 243-250. MR0761540
  5. Exchange properties in lattices of finite length, Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe 31 (1982), 15-26. Zbl0548.06003MR0693283
  6. Semimodularity in lattices of finite length, Discrete Math. 41 (1982), 287-293. Zbl0655.06006MR0676890
  7. Characterizations of semimodularity, Studia Sci. Math. Hungar. 25 (1990), 93-96. Zbl0629.06007MR1102200
  8. Semimodular Lattices, B. G. Teubner Verlagsgesellschaft, Stuttgart-Leipzig, 1991. Zbl0957.06008MR1164868

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