Varieties of De Morgan Monoids: Minimality and Irreducible Algebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F19%3A00497034" target="_blank" >RIV/67985807:_____/19:00497034 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jpaa.2018.09.015" target="_blank" >http://dx.doi.org/10.1016/j.jpaa.2018.09.015</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jpaa.2018.09.015" target="_blank" >10.1016/j.jpaa.2018.09.015</a>

Result language
angličtina
Original language name
Varieties of De Morgan Monoids: Minimality and Irreducible Algebras
Original language description
It is proved that every finitely subdirectly irreducible De Morgan monoid A (with neutral element e) is either (i) a Sugihara chain in which e covers ¬e or (ii) the union of an interval subalgebra [¬a, a] and two chains of idempotents, (¬a] and [a), where a = (¬e)2. In the latter case, the variety generated by [¬a, a] has no nontrivial idempotent member, and A/[¬a) is a Sugihara chain in which ¬e = e. It is also proved that there are just four minimal varieties of De Morgan monoids. These findings are then used to simplify the proof of a description (due to K. Świrydowicz) of the lower part of the subvariety lattice of relevant algebras. The results throw light on the models and the axiomatic extensions of fundamental relevance logics.
Czech name
—
Czech description
—

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

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)