| Title:
|
Some properties of the weak subalgebra lattice of a partial algebra of a fixed type (English) |
| Author:
|
Pióro, Konrad |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
38 |
| Issue:
|
2 |
| Year:
|
2002 |
| Pages:
|
81-94 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate, using results from [[p3]], when a given lattice is isomorphic to the weak subalgebra lattice of a partial algebra of a fixed type. First, we reduce this problem to the question when hyperedges of a hypergraph can be directed to a form of directed hypergraph of a fixed type. Secondly, we show that it is enough to consider some special hypergraphs. Finally, translating these results onto the lattice language, we obtain necessary conditions for our algebraic problem, and also, we completely characterize the weak subalgebra lattice for algebras of some types. (English) |
| Keyword:
|
hypergraph |
| Keyword:
|
weak subalgebra |
| Keyword:
|
weak subalgebra lattice |
| Keyword:
|
partial algebra |
| MSC:
|
05C65 |
| MSC:
|
06B10 |
| MSC:
|
06B15 |
| MSC:
|
08A30 |
| MSC:
|
08A55 |
| idZBL:
|
Zbl 1069.08002 |
| idMR:
|
MR1909590 |
| . |
| Date available:
|
2008-06-06T22:29:59Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107823 |
| . |
| Reference:
|
[1] Bartol W.: Weak subalgebra lattices.Comment. Math. Univ. Carolinae 31 (1990), 405–410. Zbl 0711.08007, MR 1078473 |
| Reference:
|
[2] Bartol W., Rosselló F., Rudak L.: Lectures on Algebras, Equations and Partiality.Technical report B–006, Univ. Illes Balears, Dept. Ciencies Mat. Inf., ed. Rosselló F., 1992. |
| Reference:
|
[3] Berge C.: Graphs and Hypergraphs.North-Holland, Amsterdam 1973. Zbl 0254.05101, MR 0357172 |
| Reference:
|
[4] Burmeister P.: A Model Theoretic Oriented Approach To Partial Algebras.Akademie Verlag, Berlin, 1986. Zbl 0598.08004, MR 0854861 |
| Reference:
|
[5] Crawley P., Dilworth R. P.: Algebraic Theory of Lattices.Prentice Hall Inc., Englewood Cliffs, NJ, 1973. Zbl 0494.06001 |
| Reference:
|
[6] Grätzer G.: Universal Algebra.second edition, Springer-Verlag, New York 1979. MR 0538623 |
| Reference:
|
[7] Jónsson B.: Topics in Universal Algebra.Lecture Notes in Mathemathics 250, Springer-Verlag, 1972. MR 0345895 |
| Reference:
|
[8] Pióro K.: The weak subalgebra lattice of a partial algebra of a given finite type.Acta Sci. Math. 65 (1999), 439–460. MR 1737263 |
| Reference:
|
[9] Pióro K.: On connections between hypergraphs and algebras.Arch. Math. (Brno) 36 (2000), 45–60. MR 1751613 |
| . |
