| Title:
|
Partially ordered sets having selfdual system of intervals (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
123 |
| Issue:
|
3 |
| Year:
|
1998 |
| Pages:
|
271-278 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the present paper we deal with the existence of large homogeneous partially ordered sets having the property described in the title. (English) |
| Keyword:
|
partially ordered set |
| Keyword:
|
interval |
| Keyword:
|
selfduality |
| Keyword:
|
connectedness |
| MSC:
|
06A06 |
| idZBL:
|
Zbl 0934.06004 |
| idMR:
|
MR1645442 |
| DOI:
|
10.21136/MB.1998.126074 |
| . |
| Date available:
|
2009-09-24T21:32:04Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126074 |
| . |
| Reference:
|
[1] L. Fuchs: Partially Ordered Algebraic Systems.Pergamon Press, Oxford, 1963. Zbl 0137.02001, MR 0171864 |
| Reference:
|
[2] V. I. Igoshin: Lattices of intervals and lattices of convex sublattices of lattices.Ordered sets and lattices 6 (1980), 69-76. (In Russian.) MR 0945975 |
| Reference:
|
[3] V. I. Igoshin: Identities in interval lattices of lattices.Contributions to Lattice Theory, Coll. Math. Soc. J. Bolyai 33 (1983), 491-501. Zbl 0522.06005, MR 0724279 |
| Reference:
|
[4] V. I. Igoshin: On lattices with restrictions on their interval lattices.Lectures in Universal Algebra, Coll. Math. Soc. J. Bolyai 43 (1986), 209-210. Zbl 0598.06003, MR 0860266 |
| Reference:
|
[5] V. I. Igoshin: Algebraic characterization of interval lattices.Uspechi matem. nauk 40 (1985), 205-206. (In Russian.) Zbl 0592.06002, MR 0795195 |
| Reference:
|
[6] V. I. Igoshin: Interval properties of quasivarieties of lattices.XVII. Vsesoyuz. alg. konf., Kishinev, 1985, Summaries of lectures, p. 212. (In Russian.) |
| Reference:
|
[7] V. I. Igoshin: Semimodularity in interval lattices.Math. Slovaca 38 (1988), 305-308. Zbl 0664.06007, MR 0978760 |
| Reference:
|
[8] V. I. Igoshin: Selfduality of lattices of intervals of finite lattices.International conference on algebra dedicated to the memory of A. I. Maltsev, Summaries of lectures on model theory and algebraic systems. Novosibirsk. 1989, p. 48. (In Russian.) |
| Reference:
|
[9] J. Jakubík: Selfduality of the system of intervals of a partially ordered set.Czechoslovak Math. J. 41 (1991), 135-140. MR 1087633 |
| Reference:
|
[10] J. Jakubík J. Lihová: Systems of intervals of partially ordered sets.Math. Slovaca 46 (1996), 355-361. MR 1472629 |
| Reference:
|
[11] M. Kolibiar: Intervals, convex sublattices and subdirect representations of lattices.Universal Algebra and Applications, Banach Center Publ. Vol. 9. Warsaw, 1982, pp. 335-339. Zbl 0506.06003, MR 0738826 |
| Reference:
|
[12] J. Lihová: Posets having a selfdual interval poset.Czechoslovak Math. J. 44 (1994), 523-533. MR 1288170 |
| Reference:
|
[13] V. Slavík: On lattices with isomorphic interval lattices.Czechoslovak Math. J. 35 (1985), 550-554. MR 0809041 |
| . |
