Varieties of MV-monoids and positive MV-algebras
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10509716" target="_blank" >RIV/00216208:11320/25:10509716 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=NNmQ7TTcfM" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=NNmQ7TTcfM</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jalgebra.2025.04.027" target="_blank" >10.1016/j.jalgebra.2025.04.027</a>
Alternative languages
Result language
angličtina
Original language name
Varieties of MV-monoids and positive MV-algebras
Original language description
MV-monoids are algebras < A, boolean OR, boolean AND, circle plus, circle dot,0, 1 > where < A, boolean OR, boolean AND, 0, 1 > is a bounded distributive lattice, both < A, circle plus, 0 > and < A, circle dot, 1 > are commutative monoids, and some further connecting axioms are satisfied. Every MV-algebra in the signature {circle plus, (sic), 0} is term equivalent to an algebra that has an MV-monoid as a reduct, by defining, as standard, 1 := (sic)0, x circle dot y := (sic)((sic)x circle plus(sic)y), x boolean OR y := (x circle dot(sic)y)circle plus y and x boolean AND y := (sic)((sic)x boolean OR(sic)y). Particular examples of MV-monoids are positive MV-algebras, i.e., the {boolean OR, boolean AND, circle plus, circle dot, 0, 1}-subreducts of MV-algebras. Positive MV-algebras form a peculiar quasivariety in the sense that, albeit having a logical motivation (being the quasivariety of subreducts of MV-algebras), it is not the equivalent quasivariety semantics of any logic. In this paper, we study the lattices of subvarieties of MVmonoids and of positive MV-algebras. In particular, we characterize and axiomatize all almost minimal varieties of MVmonoids, we characterize the finite subdirectly irreducible positive MV-algebras, and we characterize and axiomatize all varieties of positive MV-algebras. (c) 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Algebra
ISSN
0021-8693
e-ISSN
1090-266X
Volume of the periodical
677
Issue of the periodical within the volume
1 September 2025
Country of publishing house
US - UNITED STATES
Number of pages
55
Pages from-to
690-744
UT code for WoS article
001509465900001
EID of the result in the Scopus database
2-s2.0-105004346962