Sheffer operation in relational structures
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73614851" target="_blank" >RIV/61989592:15310/22:73614851 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s00500-021-06466-x" target="_blank" >https://link.springer.com/article/10.1007/s00500-021-06466-x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00500-021-06466-x" target="_blank" >10.1007/s00500-021-06466-x</a>
Alternative languages
Result language
angličtina
Original language name
Sheffer operation in relational structures
Original language description
The concept of a Sheffer operation known for Boolean algebras and orthomodular lattices is extended to arbitrary directed relational systems with involution. It is proved that to every such relational system, there can be assigned a Sheffer groupoid and also, conversely, every Sheffer groupoid induces a directed relational system with involution. Hence, investigations of these relational systems can be transformed to the treatment of special groupoids which form a variety of algebras. If the Sheffer operation is also commutative, then the induced binary relation is antisymmetric. Moreover, commutative Sheffer groupoids form a congruence distributive variety. We characterize symmetry, antisymmetry and transitivity of binary relations by identities and quasi-identities satisfied by an assigned Sheffer operation. The concepts of twist products of relational systems and of Kleene relational systems are introduced. We prove that every directed relational system can be embedded into a directed relational system with involution via the twist product construction. If the relation in question is even transitive, then the directed relational system can be embedded into a Kleene relational system. Any Sheffer operation assigned to a directed relational system A with involution induces a Sheffer operation assigned to the twist product of A.
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/GF20-09869L" target="_blank" >GF20-09869L: The many facets of orthomodularity</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SOFT COMPUTING
ISSN
1432-7643
e-ISSN
1433-7479
Volume of the periodical
26
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
9
Pages from-to
89-97
UT code for WoS article
000719750300004
EID of the result in the Scopus database
2-s2.0-85119176692