Semilinear De Morgan monoids and epimorphisms
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F24%3A00603653" target="_blank" >RIV/67985807:_____/24:00603653 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00012-023-00837-1" target="_blank" >https://doi.org/10.1007/s00012-023-00837-1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00012-023-00837-1" target="_blank" >10.1007/s00012-023-00837-1</a>
Alternative languages
Result language
angličtina
Original language name
Semilinear De Morgan monoids and epimorphisms
Original language description
A representation theorem is proved for De Morgan monoids that are (i) semilinear, i.e., subdirect products of totally ordered algebras, and (ii) negatively generated, i.e., generated by lower bounds of the neutral element. Using this theorem, we prove that the De Morgan monoids satisfying (i) and (ii) form a variety-in fact, a locally finite variety. We then prove that epimorphisms are surjective in every variety of negatively generated semilinear De Morgan monoids. In the process, epimorphism-surjectivity is established for several other classes as well, including the variety of all semilinear idempotent commutative residuated lattices and all varieties of negatively generated semilinear Dunn monoids. The results settle natural questions about Beth-style definability for a range of substructural logics.
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/EF18_053%2F0017594" target="_blank" >EF18_053/0017594: Supporting the internationalization of the Institute of Computer Science of the Czech Academy of Sciences</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Algebra Universalis
ISSN
0002-5240
e-ISSN
1420-8911
Volume of the periodical
85
Issue of the periodical within the volume
1
Country of publishing house
DE - GERMANY
Number of pages
34
Pages from-to
10
UT code for WoS article
001138568500001
EID of the result in the Scopus database
2-s2.0-85181652531