| Title:
|
A visual approach to test lattices (English) |
| Author:
|
Czédli, Gábor |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
48 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
33-52 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $p$ be a $k$-ary lattice term. A $k$-pointed lattice $L=(L;\vee ,\wedge $, $d_1,\ldots ,d_k)$ will be called a $p$-lattice (or a test lattice if $p$ is not specified), if $(L;\vee ,\wedge )$ is generated by $\lbrace d_1,\ldots ,d_k\rbrace $ and, in addition, for any $k$-ary lattice term $q$ satisfying $p(d_1,\ldots ,d_k)$ $\le $ $q(d_1$, $\ldots , d_k)$ in $L$, the lattice identity $p\le q$ holds in all lattices. In an elementary visual way, we construct a finite $p$-lattice $L(p)$ for each $p$. If $p$ is a canonical lattice term, then $L(p)$ coincides with the optimal $p$-lattice of Freese, Ježek and Nation [Freese, R., Ježek, J., Nation, J. B.: Free lattices. American Mathematical Society, Providence, RI, Mathematical Surveys and Monographs 42, 1995, viii+293 pp.]. Some results on test lattices and short proofs for known facts on free lattices indicate that our approach is useful. (English) |
| Keyword:
|
Free lattice |
| Keyword:
|
test lattice |
| Keyword:
|
lattice identity |
| Keyword:
|
Whitman’s condition |
| MSC:
|
06B25 |
| idZBL:
|
Zbl 1203.06011 |
| idMR:
|
MR2641946 |
| . |
| Date available:
|
2010-02-11T13:54:45Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137512 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
