Adjoint operations in twist-products of lattices

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F21%3A73609271" target="_blank" >RIV/61989592:15310/21:73609271 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.mdpi.com/2073-8994/13/2/253/htm" target="_blank" >https://www.mdpi.com/2073-8994/13/2/253/htm</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/sym13020253" target="_blank" >10.3390/sym13020253</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Adjoint operations in twist-products of lattices

Popis výsledku v původním jazyce

Given an integral commutative residuated lattices L = (L, V, A), its full twist-product (L-2, (sic), (sic)) can be endowed with two binary operations circle dot and double right arrow introduced formerly by M. Busaniche and R. Cignoli as well as by C. Tsinakis and A. M. Wille such that it becomes a commutative residuated lattice. For every a is an element of L we define a certain subset P-a (L) of L-2. We characterize when Pa(L) is a sublattice of the full twist-product (L-2, (sic), (sic)). In this case P-a( L) together with some natural antitone involution &apos; ecomes a pseudo-Kleene lattice. If L is distributive then (P-a(L), (sic), (sic), &apos;) becomes a Kleene lattice. We present sufficient conditions for P-a(L) being a subalgebra of (L-2,(sic), (sic), circle dot, double right arrow) and thus for and) being a pair of adjoint operations on P-a(L). Finally, we introduce another pair circle dot and double right arrow of adjoint operations on the full twist-product of a bounded commutative residuated lattice such that the resulting algebra is a bounded commutative residuated lattice satisfying the double negation law, and we investigate when P-a(L) is closed under these new operations.

Název v anglickém jazyce

Adjoint operations in twist-products of lattices

Popis výsledku anglicky

Given an integral commutative residuated lattices L = (L, V, A), its full twist-product (L-2, (sic), (sic)) can be endowed with two binary operations circle dot and double right arrow introduced formerly by M. Busaniche and R. Cignoli as well as by C. Tsinakis and A. M. Wille such that it becomes a commutative residuated lattice. For every a is an element of L we define a certain subset P-a (L) of L-2. We characterize when Pa(L) is a sublattice of the full twist-product (L-2, (sic), (sic)). In this case P-a( L) together with some natural antitone involution &apos; ecomes a pseudo-Kleene lattice. If L is distributive then (P-a(L), (sic), (sic), &apos;) becomes a Kleene lattice. We present sufficient conditions for P-a(L) being a subalgebra of (L-2,(sic), (sic), circle dot, double right arrow) and thus for and) being a pair of adjoint operations on P-a(L). Finally, we introduce another pair circle dot and double right arrow of adjoint operations on the full twist-product of a bounded commutative residuated lattice such that the resulting algebra is a bounded commutative residuated lattice satisfying the double negation law, and we investigate when P-a(L) is closed under these new operations.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GF20-09869L" target="_blank" >GF20-09869L: Ortomodularita z různých pohledů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Symmetry-Basel

ISSN

2073-8994

e-ISSN

—

Svazek periodika

13

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

13

Strana od-do

"253 "- 265

Kód UT WoS článku

000623197000001

EID výsledku v databázi Scopus

2-s2.0-85100533570