Simplified axiomatic system of DRl-semigroups

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216275%3A25410%2F25%3A39923311" target="_blank" >RIV/00216275:25410/25:39923311 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1515/ms-2025-0053" target="_blank" >https://doi.org/10.1515/ms-2025-0053</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/ms-2025-0053" target="_blank" >10.1515/ms-2025-0053</a>

Result language
angličtina
Original language name
Simplified axiomatic system of DRl-semigroups
Original language description
DRl-semigroups are a generalization of lattice ordered groups (l-groups) containing a.o. Boolean algebras, Brouwerian algebras and MV-algebras. Since their introduction in the 1960s their axiomatic system has been several times reduced.In this paper, we show that it can be simplified even further. Specifically, we show that the axiom ensuring compatibility of the semigroup operation + and the lattice operations is equivalent to a significantly weaker condition of monotonicity of + with respect to the implied order <=. Because the same equivalence holds for l-groups, we observe that the axiomatic systems of l-groups and DRl-semigroups are more aligned than originally thought.
Czech name
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Czech description
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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

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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