| Title:
|
$\delta$-ideals in pseudo-complemented distributive lattices (English) |
| Author:
|
Sambasiva Rao, M. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
48 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
97-105 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The concept of $\delta$-ideals is introduced in a pseudo-complemented distributive lattice and some properties of these ideals are studied. Stone lattices are characterized in terms of $\delta$-ideals. A set of equivalent conditions is obtained to characterize a Boolean algebra in terms of $\delta$-ideals. Finally, some properties of $\delta$-ideals are studied with respect to homomorphisms and filter congruences. (English) |
| Keyword:
|
pseudo-complemented distributive lattice |
| Keyword:
|
dense element |
| Keyword:
|
closed element |
| Keyword:
|
$\delta$-ideal |
| Keyword:
|
Stone lattice |
| Keyword:
|
congruence |
| MSC:
|
06D15 |
| MSC:
|
06D99 |
| idMR:
|
MR2946209 |
| DOI:
|
10.5817/AM2012-2-97 |
| . |
| Date available:
|
2012-06-08T08:30:51Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142823 |
| . |
| Reference:
|
[1] Balbes, R., Horn, A.: Stone lattices.Duke Math. J. 37 (1970), 537–545. Zbl 0207.02802, MR 0277448 |
| Reference:
|
[2] Birkhoff, G.: Lattice Theory.Colloquium Publications, vol. 25, Amer. Math. Soc., New York, 1948. Zbl 0033.10103, MR 0029876 |
| Reference:
|
[3] Cornish, W. H.: Congruences on distributive pseudocomplemented lattices.Bull. Austral. Math. Soc. 8 (1973), 161–179. Zbl 0251.06018, MR 0318024, 10.1017/S0004972700042404 |
| Reference:
|
[4] Frink, O.: Pseudo-complements in semi-lattices.Duke Math. J. 29 (1962), 505–514. Zbl 0114.01602, MR 0140449, 10.1215/S0012-7094-62-02951-4 |
| Reference:
|
[5] Grätzer, G.: A generalization on Stone’s representation theorem for Boolean algebras.Duke Math. J. 30 (1963), 469–474. MR 0153605, 10.1215/S0012-7094-63-03051-5 |
| Reference:
|
[6] Grätzer, G.: General lattice theory.Academic Press, New York, San Francisco, 1978. Zbl 0436.06001, MR 0509213 |
| Reference:
|
[7] Speed, T. P.: Two congruences on distributive lattices.Bull. Soc. Roy. Sci. Liège 38 (3–4) (1969), 86–95. Zbl 0176.28504, MR 0245489 |
| Reference:
|
[8] Speed, T. P.: Spaces of ideals of distributive lattices II. Minimal prime ideals.J. Austral. Math. Soc. 18 (1974), 54–72. Zbl 0294.06009, MR 0354476, 10.1017/S144678870001911X |
| . |
