Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 506-515 |
| Seitenumfang | 10 |
| Fachzeitschrift | Algebra universalis |
| Jahrgang | 31 |
| Ausgabenummer | 4 |
| Publikationsstatus | Veröffentlicht - Dez. 1994 |
Abstract
We investigate various weak conditions ensuring that a lattice be complemented. Using these general results in connection with a famous result due to Lampe, we show that the lattice of all equational theories containing a fixed theory must be complemented if it is lower semicomplemented, thereby answering in the affirmative a question raised by Volkov and Vernikov. Moreover, such a lattice must be a finite Boolean algebra if it has one of the following properties: upper or lower sectionally complemented; incomparably complemented; lower semicomplemented and lower semimodular; or atomistic and upper semimodular.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Algebra und Zahlentheorie
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in: Algebra universalis, Jahrgang 31, Nr. 4, 12.1994, S. 506-515.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Complements in lattices of varieties and equational theories
AU - Diercks, V.
AU - Erné, M.
AU - Reinhold, J.
PY - 1994/12
Y1 - 1994/12
N2 - We investigate various weak conditions ensuring that a lattice be complemented. Using these general results in connection with a famous result due to Lampe, we show that the lattice of all equational theories containing a fixed theory must be complemented if it is lower semicomplemented, thereby answering in the affirmative a question raised by Volkov and Vernikov. Moreover, such a lattice must be a finite Boolean algebra if it has one of the following properties: upper or lower sectionally complemented; incomparably complemented; lower semicomplemented and lower semimodular; or atomistic and upper semimodular.
AB - We investigate various weak conditions ensuring that a lattice be complemented. Using these general results in connection with a famous result due to Lampe, we show that the lattice of all equational theories containing a fixed theory must be complemented if it is lower semicomplemented, thereby answering in the affirmative a question raised by Volkov and Vernikov. Moreover, such a lattice must be a finite Boolean algebra if it has one of the following properties: upper or lower sectionally complemented; incomparably complemented; lower semicomplemented and lower semimodular; or atomistic and upper semimodular.
UR - http://www.scopus.com/inward/record.url?scp=34249772938&partnerID=8YFLogxK
U2 - 10.1007/BF01236502
DO - 10.1007/BF01236502
M3 - Article
AN - SCOPUS:34249772938
VL - 31
SP - 506
EP - 515
JO - Algebra universalis
JF - Algebra universalis
SN - 0002-5240
IS - 4
ER -