| Title:
|
Distributive lattices have the intersection property (English) |
| Author:
|
Mühle, Henri |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
146 |
| Issue:
|
1 |
| Year:
|
2021 |
| Pages:
|
7-17 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Distributive lattices form an important, well-behaved class of lattices. They are instances of two larger classes of lattices: congruence-uniform and semidistributive lattices. Congruence-uniform lattices allow for a remarkable second order of their elements: the core label order; semidistributive lattices naturally possess an associated flag simplicial complex: the canonical join complex. In this article we present a characterization of finite distributive lattices in terms of the core label order and the canonical join complex, and we show that the core label order of a finite distributive lattice is always a meet-semilattice. (English) |
| Keyword:
|
distributive lattice |
| Keyword:
|
congruence-uniform lattice |
| Keyword:
|
canonical join complex |
| Keyword:
|
core label order |
| Keyword:
|
intersection property |
| MSC:
|
06D05 |
| idZBL:
|
07332739 |
| idMR:
|
MR4227308 |
| DOI:
|
10.21136/MB.2019.0156-18 |
| . |
| Date available:
|
2021-03-12T16:17:36Z |
| Last updated:
|
2021-04-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148744 |
| . |
| Reference:
|
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