The variety of complemented lattices where conjunction and implication form an adjoint pair

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F25%3A73633301" target="_blank" >RIV/61989592:15310/25:73633301 - isvavai.cz</a>

Výsledek na webu

<a href="https://academic.oup.com/logcom/article/35/4/exaf024/8121701" target="_blank" >https://academic.oup.com/logcom/article/35/4/exaf024/8121701</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1093/logcom/exaf024" target="_blank" >10.1093/logcom/exaf024</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The variety of complemented lattices where conjunction and implication form an adjoint pair

Popis výsledku v původním jazyce

The Sasaki projection was introduced as a mapping from the lattice of closed subspaces of a Hilbert space onto one of its segments. To use this projection and its dual so-called Sasaki operations were introduced by the second two authors in [4] and [6]. In [6] there are described several classes of lattices, λ-lattices and semirings where the Sasaki operations form an adjoint pair. In the present paper we prove that the class of complemented lattices with this property forms a variety and we explicitly state its defining identities. Moreover, we prove that this variety V is congruence permutable and regular. Hence every ideal I of some member L of V is a kernel of some congruence on L. Finally, we determine a finite basis of so-called ideal terms and describe the congruence ΘI determined by the ideal I.

Název v anglickém jazyce

The variety of complemented lattices where conjunction and implication form an adjoint pair

Popis výsledku anglicky

The Sasaki projection was introduced as a mapping from the lattice of closed subspaces of a Hilbert space onto one of its segments. To use this projection and its dual so-called Sasaki operations were introduced by the second two authors in [4] and [6]. In [6] there are described several classes of lattices, λ-lattices and semirings where the Sasaki operations form an adjoint pair. In the present paper we prove that the class of complemented lattices with this property forms a variety and we explicitly state its defining identities. Moreover, we prove that this variety V is congruence permutable and regular. Hence every ideal I of some member L of V is a kernel of some congruence on L. Finally, we determine a finite basis of so-called ideal terms and describe the congruence ΘI determined by the ideal I.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

JOURNAL OF LOGIC AND COMPUTATION

ISSN

0955-792X

e-ISSN

1465-363X

Svazek periodika

35

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

10

Strana od-do

"exaf024-1"-"exaf024-10"

Kód UT WoS článku

001477997800001

EID výsledku v databázi Scopus

2-s2.0-105004265877