On the Coextension of Cut-Continuous Pomonoids

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F19%3A00107993" target="_blank" >RIV/00216224:14310/19:00107993 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007%2Fs11083-018-9466-3" target="_blank" >https://link.springer.com/article/10.1007%2Fs11083-018-9466-3</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11083-018-9466-3" target="_blank" >10.1007/s11083-018-9466-3</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the Coextension of Cut-Continuous Pomonoids

Popis výsledku v původním jazyce

We introduce cut-continuous pomonoids, which generalise residuated posets. The latter's defining condition is that the monoidal product is residuated in each argument; we define cut-continuous pomonoids by requiring that the monoidal product is in each argument just cut-continuous. In the case of a total order, the condition of cut-continuity means that multiplication distributes over existing suprema. Morphisms between cut-continuous pomonoids can be chosen either in analogy with unital quantales or with residuated lattices. Under the assumption of commutativity and integrality, congruences are in the latter case induced by filters, in the same way as known for residuated lattices. We are interested in the construction of coextensions: given cut-continuous pomonoids K and C, we raise the question how we can determine the cut-continuous pomonoids L such that C is a filter of L and the quotient of L induced by C is isomorphic to K. In this context, we are in particular concerned with tensor products of modules over cut-continuous pomonoids. Using results of M. Erne and J. Picado on closure spaces, we show that such tensor products exist. An application is the construction of residuated structures related to fuzzy logics, in particular left-continuous t-norms.

Název v anglickém jazyce

On the Coextension of Cut-Continuous Pomonoids

Popis výsledku anglicky

We introduce cut-continuous pomonoids, which generalise residuated posets. The latter's defining condition is that the monoidal product is residuated in each argument; we define cut-continuous pomonoids by requiring that the monoidal product is in each argument just cut-continuous. In the case of a total order, the condition of cut-continuity means that multiplication distributes over existing suprema. Morphisms between cut-continuous pomonoids can be chosen either in analogy with unital quantales or with residuated lattices. Under the assumption of commutativity and integrality, congruences are in the latter case induced by filters, in the same way as known for residuated lattices. We are interested in the construction of coextensions: given cut-continuous pomonoids K and C, we raise the question how we can determine the cut-continuous pomonoids L such that C is a filter of L and the quotient of L induced by C is isomorphic to K. In this context, we are in particular concerned with tensor products of modules over cut-continuous pomonoids. Using results of M. Erne and J. Picado on closure spaces, we show that such tensor products exist. An application is the construction of residuated structures related to fuzzy logics, in particular left-continuous t-norms.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF15-34697L" target="_blank" >GF15-34697L: Nové přístupy k reziduovaným posetům</a><br>

Návaznosti

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

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS

ISSN

0167-8094

e-ISSN

1572-9273

Svazek periodika

36

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

20

Strana od-do

271-290

Kód UT WoS článku

000476618800007

EID výsledku v databázi Scopus

2-s2.0-85051476485