On duality of submodule lattices

• Autorzy: Gábor Czédli , Géza Takách
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

submodule lattice; lattice identity; duality

Kategorie tematyczne

• 16D99: None of the above, but in this section
• 06C05: Modular lattices, Desarguesian lattices
• 08B10: Congruence modularity, congruence distributivity

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2000
• Tom: 20
• Numer: 1
• Strony: 43-49

Daty

wydano

2000

otrzymano

1998-04-23

Twórcy

autor

Gábor Czédli

• JATE Bolyai Institute, Aradi vértanúk tere 1, H-6720 Szeged, Hungary

autor

Géza Takách

• JATE Bolyai Institute, Aradi vértanúk tere 1, H-6720 Szeged, Hungary

Bibliografia

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

Identyfikatory

DOI

10.7151/dmgaa.1004