On duality of submodule lattices

Gábor Czédli; Géza Takách

Discussiones Mathematicae - General Algebra and Applications (2000)

  • Volume: 20, Issue: 1, page 43-49
  • ISSN: 1509-9415

Abstract

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An elementary proof is given for Hutchinson's duality theorem, which states that if a lattice identity λ holds in all submodule lattices of modules over a ring R with unit element then so does the dual of λ.

How to cite

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Gábor Czédli, and Géza Takách. "On duality of submodule lattices." Discussiones Mathematicae - General Algebra and Applications 20.1 (2000): 43-49. <http://eudml.org/doc/287620>.

@article{GáborCzédli2000,
abstract = {An elementary proof is given for Hutchinson's duality theorem, which states that if a lattice identity λ holds in all submodule lattices of modules over a ring R with unit element then so does the dual of λ.},
author = {Gábor Czédli, Géza Takách},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {submodule lattice; lattice identity; duality; subgroup lattices of finite Abelian groups},
language = {eng},
number = {1},
pages = {43-49},
title = {On duality of submodule lattices},
url = {http://eudml.org/doc/287620},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Gábor Czédli
AU - Géza Takách
TI - On duality of submodule lattices
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2000
VL - 20
IS - 1
SP - 43
EP - 49
AB - An elementary proof is given for Hutchinson's duality theorem, which states that if a lattice identity λ holds in all submodule lattices of modules over a ring R with unit element then so does the dual of λ.
LA - eng
KW - submodule lattice; lattice identity; duality; subgroup lattices of finite Abelian groups
UR - http://eudml.org/doc/287620
ER -

References

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  1. [1] G. Frobenius, Theorie der linearen Formen mit ganzen Coefficienten, J. Reine Angew. Math. 86 (1879), 146-208. Zbl10.0079.02
  2. [2] G. Hutchinson, On classes of lattices representable by modules, Proceedings of the University of Houston Lattice Theory Conference, Univ. Houston 1973, 69-94. Zbl0302.06016
  3. [3] G. Hutchinson and G. Czédli, A test for identities satisfied in submodule lattices, Algebra Universalis 8 (1978), 269-309. Zbl0384.06009
  4. [4] A.F. Pixley, Local Mal'cev conditions, Canadian Math. Bull. 15 (1972), 559-568. Zbl0254.08009
  5. [5] R. Wille, Kongruenzklassengeometrien, Lecture Notes in Math, no. 113, Springer-Verlag, Berlin-Heidelberg-New York 1970. 

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