Convex isomorphisms of directed multilattices

Ján Jakubík; Mária Csontóová

Mathematica Bohemica (1993)

  • Volume: 118, Issue: 4, page 359-378
  • ISSN: 0862-7959

Abstract

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By applying the solution of the internal direct product decomposition we investigate the relations between convex isomorphisms and direct product decompositions of directed multilattices.

How to cite

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Jakubík, Ján, and Csontóová, Mária. "Convex isomorphisms of directed multilattices." Mathematica Bohemica 118.4 (1993): 359-378. <http://eudml.org/doc/29311>.

@article{Jakubík1993,
abstract = {By applying the solution of the internal direct product decomposition we investigate the relations between convex isomorphisms and direct product decompositions of directed multilattices.},
author = {Jakubík, Ján, Csontóová, Mária},
journal = {Mathematica Bohemica},
keywords = {direct product decomposition; convex isomorphisms; directed multilattices; directly indecomposable lattices; internal direct product decomposition; directed set; multilattice; direct product decomposition; convex isomorphisms; directed multilattices; directly indecomposable lattices},
language = {eng},
number = {4},
pages = {359-378},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Convex isomorphisms of directed multilattices},
url = {http://eudml.org/doc/29311},
volume = {118},
year = {1993},
}

TY - JOUR
AU - Jakubík, Ján
AU - Csontóová, Mária
TI - Convex isomorphisms of directed multilattices
JO - Mathematica Bohemica
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 118
IS - 4
SP - 359
EP - 378
AB - By applying the solution of the internal direct product decomposition we investigate the relations between convex isomorphisms and direct product decompositions of directed multilattices.
LA - eng
KW - direct product decomposition; convex isomorphisms; directed multilattices; directly indecomposable lattices; internal direct product decomposition; directed set; multilattice; direct product decomposition; convex isomorphisms; directed multilattices; directly indecomposable lattices
UR - http://eudml.org/doc/29311
ER -

References

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  1. M. Benado, Sur la théorie de la divisibilité, Acad. R. P. Romine, Bul. Sti. Sect. Mat. Fiz. 6 (1954), 263-270. (1954) Zbl0057.25301MR0067089
  2. C. C. Chen M. K. Koh, On the lattice of convex sublattices of a finite lattice, Nanta Math. 5 (1972), 93-95. (1972) MR0351934
  3. J. Hashimoto, 10.2307/1969532, Annals of Math. 54 (1951), 315-318. (1951) MR0043067DOI10.2307/1969532
  4. J. Jakubík M. Kolibiar, On some properties of pairs of lattices, Czechoslov. Math. J. 4 (1954), 1-27. (In Russian.) (1954) MR0065529
  5. M. Kolibiar, 10.4064/-9-1-335-339, Universal algebra and applications, Banach Center Publications, Vol. 9, Warszawa, 1980, pp. 335-339. (1980) MR0738826DOI10.4064/-9-1-335-339
  6. M. Kolibiar J. Lihová, Convex automorphisms of a lattice, Math. Slovaca, to appear. MR1248975
  7. A. G. Kurosh, Group Theory, Third edition, Moskva, 1967. (In Russian.) (1967) Zbl0189.30801
  8. V. I. Marmazeev, The lattice of convex sublattices of a lattice, Ordered sets and lattices No. 9, Saratov. Gos. Univ., Saratov, 1986, pp. 50-58. (In Russian.) (1986) Zbl0711.06005MR0957970
  9. V. I. Marmazeev, A group of automorphisms of the lattice of convex sublattices of a lattice, Vestsi Akad. Navuk BSSR, Ser. fiz. mat. navuk (1988), no. 6, 110-112. (In Russian, English summary.) (1988) MR0984119

Citations in EuDML Documents

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  1. Ján Jakubík, Graph automorphisms of a finite modular lattice
  2. Ján Jakubík, Mária Csontóová, Cancellation rule for internal direct product decompositions of a connected partially ordered set
  3. Ján Jakubík, Judita Lihová, On the cancellation law for disconnected partially ordered sets
  4. Ján Jakubík, Atomicity of the Boolean algebra of direct factors of a directed set
  5. Ján Jakubík, Graph automorphisms and cells of lattices
  6. Ján Jakubík, On direct and subdirect product decompositions of partially ordered sets
  7. Judita Lihová, Weak direct factors of lattices
  8. Ján Jakubík, Graph automorphisms of semimodular lattices
  9. Ján Jakubík, On a cancellation rule for subdirect products of lattice ordered groups and of GMV -algebras
  10. Ján Jakubík, Direct product decompositions of infinitely distributive lattices

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