On the Coextension of Cut-Continuous Pomonoids

J 2019

On the Coextension of Cut-Continuous Pomonoids

KRUML, David; Jan PASEKA a Thomas VETTERLEIN

Základní údaje

Originální název

On the Coextension of Cut-Continuous Pomonoids

Autoři

KRUML, David; Jan PASEKA a Thomas VETTERLEIN

Vydání

ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, DORDRECHT, SPRINGER, 2019, 0167-8094

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Nizozemské království

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.576

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/19:00107993

Organizační jednotka

Přírodovědecká fakulta

DOI

https://doi.org/10.1007/s11083-018-9466-3

UT WoS

000476618800007

EID Scopus

2-s2.0-85051476485

Klíčová slova anglicky

Partially ordered monoid; Cut-continuous pomonoid; Residuated poset; Coextension of cut-continuous pomonoids; Tensor product of modules over cut-continuous pomonoids; Closure space

Štítky

rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 28. 3. 2020 15:22, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

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.

Návaznosti

GF15-34697L, projekt VaV

Název: Nové přístupy k reziduovaným posetům

Investor: Grantová agentura ČR, New approaches to residuated posets, Partnerská agentura (Rakousko)

Citovat

KRUML, David; Jan PASEKA a Thomas VETTERLEIN. On the Coextension of Cut-Continuous Pomonoids. ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS. DORDRECHT: SPRINGER, 2019, roč. 36, č. 2, s. 271-290. ISSN 0167-8094. Dostupné z: https://doi.org/10.1007/s11083-018-9466-3.

@article{1601877,
   author = {Kruml, David and Paseka, Jan and Vetterlein, Thomas},
   article_location = {DORDRECHT},
   article_number = {2},
   doi = {https://doi.org/10.1007/s11083-018-9466-3},
   keywords = {Partially ordered monoid; Cut-continuous pomonoid; Residuated poset; Coextension of cut-continuous pomonoids; Tensor product of modules over cut-continuous pomonoids; Closure space},
   language = {eng},
   issn = {0167-8094},
   journal = {ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS},
   title = {On the Coextension of Cut-Continuous Pomonoids},
   url = {https://link.springer.com/article/10.1007%2Fs11083-018-9466-3},
   volume = {36},
   year = {2019}
}

TY  - JOUR
ID  - 1601877
AU  - Kruml, David - Paseka, Jan - Vetterlein, Thomas
PY  - 2019
TI  - On the Coextension of Cut-Continuous Pomonoids
JF  - ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS
VL  - 36
IS  - 2
SP  - 271-290
EP  - 271-290
PB  - SPRINGER
SN  - 01678094
KW  - Partially ordered monoid
KW  - Cut-continuous pomonoid
KW  - Residuated poset
KW  - Coextension of cut-continuous pomonoids
KW  - Tensor product of modules over cut-continuous pomonoids
KW  - Closure space
UR  - https://link.springer.com/article/10.1007%2Fs11083-018-9466-3
L2  - https://link.springer.com/article/10.1007%2Fs11083-018-9466-3
N2  - 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.
ER  -

KRUML, David; Jan PASEKA a Thomas VETTERLEIN. On the Coextension of Cut-Continuous Pomonoids. \textit{ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS}. DORDRECHT: SPRINGER, 2019, roč.~36, č.~2, s.~271-290. ISSN~0167-8094. Dostupné z: https://doi.org/10.1007/s11083-018-9466-3.

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