On the Coextension of Cut-Continuous Pomonoids
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
On the Coextension of Cut-Continuous Pomonoids
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GF15-34697L" target="_blank" >GF15-34697L: New perspectives on residuated posets</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS
ISSN
0167-8094
e-ISSN
1572-9273
Volume of the periodical
36
Issue of the periodical within the volume
2
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
20
Pages from-to
271-290
UT code for WoS article
000476618800007
EID of the result in the Scopus database
2-s2.0-85051476485