A few notes on subalgebra lattices, Part II

• Autorzy: Pióro, K.
• Języki publikacji: EN

Abstrakty

EN

First, we give another, simpler and shorter, proof of the weak subalgebra lattice characterization theorem formulated in [Bar]. Secondly, we apply this result and also facts from [Pió1] to characterize the weak subalgebra lattice of a partial monounary algebra. Using this characterization and results from the previous part [Pió2] we describe all pairs of lattices (L1, L2) for which there is a partial monounary algebra having its weak and strong subalgebra lattices isomorphic to L1 and L2, respectively.

Słowa kluczowe

EN

subalgebra; subalgebra lattices

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 1
• Strony: 32-42
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Pióro, K.

• Institute of Mathematics Warsaw University ul. Banacha 2 02-097 Warsaw, Poland,

Bibliografia

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• [3] C. Berge , Graphs and Hypergraphs, North-Holland, Amsterdam 1973.
• [4] P. Burmeister , A Model Theoretic Oriented Approach To Partial Algebras, Math. Research Band 32, Akademie Verlag, Berlin, 1986.
• [5] P. Crawley and R. P. Dilworth , Algebraic Theory of Lattices, Prentice Hall Inc., Englewood Cliffs, NJ, 1973.
• [6] J. Johnson and R. L. Seifer, A survey of multi-unary algebras, Mimeographed seminar notes, U.C. Berkeley, 1967.
• [7] B. Jonsson , Topics in Universal Algebra, Lecture Notes in Mathemathics 250, Springer, 1972.
• [8] K. Pióro , On some non-obvious connections between graphs and partial unary algebras, Czechoslovak Math. J. 50 (125) (2000), 295-320.
• [9] K. Pióro , A few notes on subalgebra lattices, part I , Demonstratio Math. 33(4) (2000), 695-706.
• [10] O. Ore , Theory of Graphs, AMS Colloq. Publ. 38 (1962).