Varieties of MV-monoids and positive MV-algebras

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Varieties of MV-monoids and positive MV-algebras

Popis výsledku v původním jazyce

MV-monoids are algebras &lt; A, boolean OR, boolean AND, circle plus, circle dot,0, 1 &gt; where &lt; A, boolean OR, boolean AND, 0, 1 &gt; is a bounded distributive lattice, both &lt; A, circle plus, 0 &gt; and &lt; A, circle dot, 1 &gt; 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/).

Název v anglickém jazyce

Varieties of MV-monoids and positive MV-algebras

Popis výsledku anglicky

MV-monoids are algebras &lt; A, boolean OR, boolean AND, circle plus, circle dot,0, 1 &gt; where &lt; A, boolean OR, boolean AND, 0, 1 &gt; is a bounded distributive lattice, both &lt; A, circle plus, 0 &gt; and &lt; A, circle dot, 1 &gt; 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/).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Journal of Algebra

ISSN

0021-8693

e-ISSN

1090-266X

Svazek periodika

677

Číslo periodika v rámci svazku

1 September 2025

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

55

Strana od-do

690-744

Kód UT WoS článku

001509465900001

EID výsledku v databázi Scopus

2-s2.0-105004346962