ArticleOriginal scientific text
Title
On duality of submodule lattices
Authors 1, 1
Affiliations
- JATE Bolyai Institute, Aradi vértanúk tere 1, H-6720 Szeged, Hungary
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.
Keywords
submodule lattice, lattice identity, duality
Bibliography
- G. Frobenius, Theorie der linearen Formen mit ganzen Coefficienten, J. Reine Angew. Math. 86 (1879), 146-208.
- G. Hutchinson, On classes of lattices representable by modules, Proceedings of the University of Houston Lattice Theory Conference, Univ. Houston 1973, 69-94.
- G. Hutchinson and G. Czédli, A test for identities satisfied in submodule lattices, Algebra Universalis 8 (1978), 269-309.
- A.F. Pixley, Local Mal'cev conditions, Canadian Math. Bull. 15 (1972), 559-568.
- R. Wille, Kongruenzklassengeometrien, Lecture Notes in Math, no. 113, Springer-Verlag, Berlin-Heidelberg-New York 1970.
Pages:
43-49
Main language of publication
English
Received
1998-04-23
Published
2000
DOI: 10.7151/dmgaa.1004
Exact and natural sciences