Groupoids assigned to relational systems
Mathematica Bohemica (2013)
- Volume: 138, Issue: 1, page 15-23
- ISSN: 0862-7959
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topChajda, Ivan, and Länger, Helmut. "Groupoids assigned to relational systems." Mathematica Bohemica 138.1 (2013): 15-23. <http://eudml.org/doc/252503>.
@article{Chajda2013,
abstract = {By a relational system we mean a couple $(A,R)$ where $A$ is a set and $R$ is a binary relation on $A$, i.e. $R\subseteq A\times A$. To every directed relational system $\mathcal \{A\}=(A,R)$ we assign a groupoid $\{\mathcal \{G\}\}(\{\mathcal \{A\}\})=(A,\cdot )$ on the same base set where $xy=y$ if and only if $(x,y)\in R$. We characterize basic properties of $R$ by means of identities satisfied by $\{\mathcal \{G\}\}(\{\mathcal \{A\}\})$ and show how homomorphisms between those groupoids are related to certain homomorphisms of relational systems.},
author = {Chajda, Ivan, Länger, Helmut},
journal = {Mathematica Bohemica},
keywords = {relational system; groupoid; directed system; $g$-homomorphism; relational system; groupoid; directed system; -homomorphism},
language = {eng},
number = {1},
pages = {15-23},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Groupoids assigned to relational systems},
url = {http://eudml.org/doc/252503},
volume = {138},
year = {2013},
}
TY - JOUR
AU - Chajda, Ivan
AU - Länger, Helmut
TI - Groupoids assigned to relational systems
JO - Mathematica Bohemica
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 138
IS - 1
SP - 15
EP - 23
AB - By a relational system we mean a couple $(A,R)$ where $A$ is a set and $R$ is a binary relation on $A$, i.e. $R\subseteq A\times A$. To every directed relational system $\mathcal {A}=(A,R)$ we assign a groupoid ${\mathcal {G}}({\mathcal {A}})=(A,\cdot )$ on the same base set where $xy=y$ if and only if $(x,y)\in R$. We characterize basic properties of $R$ by means of identities satisfied by ${\mathcal {G}}({\mathcal {A}})$ and show how homomorphisms between those groupoids are related to certain homomorphisms of relational systems.
LA - eng
KW - relational system; groupoid; directed system; $g$-homomorphism; relational system; groupoid; directed system; -homomorphism
UR - http://eudml.org/doc/252503
ER -
References
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