| Title:
|
Groupoids assigned to relational systems (English) |
| Author:
|
Chajda, Ivan |
| Author:
|
Länger, Helmut |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
138 |
| Issue:
|
1 |
| Year:
|
2013 |
| Pages:
|
15-23 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
relational system |
| Keyword:
|
groupoid |
| Keyword:
|
directed system |
| Keyword:
|
$g$-homomorphism |
| MSC:
|
08A02 |
| MSC:
|
20N02 |
| idZBL:
|
Zbl 1274.08002 |
| idMR:
|
MR3076217 |
| DOI:
|
10.21136/MB.2013.143226 |
| . |
| Date available:
|
2013-03-02T18:47:17Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143226 |
| . |
| Reference:
|
[1] Chajda, I.: Congruences in transitive relational systems.Miskolc Math. Notes 5 (2004), 19-23. Zbl 1047.08001, MR 2040973, 10.18514/MMN.2004.77 |
| Reference:
|
[2] Chajda, I.: Class preserving mappings of equivalence systems.Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 43 (2004), 61-64. Zbl 1077.08001, MR 2124603 |
| Reference:
|
[3] Chajda, I.: Homomorphisms of directed posets.Asian-Eur. J. Math. 1 (2008), 45-51. Zbl 1159.06002, MR 2400299, 10.1142/S1793557108000059 |
| Reference:
|
[4] Chajda, I., Hošková, Š.: A characterization of cone preserving mappings of quasiordered sets.Miskolc Math. Notes 6 (2005), 147-152. Zbl 1095.08001, MR 2199159, 10.18514/MMN.2005.107 |
| Reference:
|
[5] Chajda, I., Länger, H.: Quotients and homomorphisms of relational systems.Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 49 (2010), 37-47. Zbl 1241.08001, MR 2796945 |
| Reference:
|
[6] Mal'cev, A. I.: Algebraic Systems.Springer, New York (1973). MR 0349384 |
| Reference:
|
[7] Pöschel, R.: Graph algebras and graph varieties.Algebra Univers. 27 (1990), 559-577. Zbl 0725.08002, MR 1387902, 10.1007/BF01189000 |
| Reference:
|
[8] Riguet, J.: Relations binaires, fermetures, correspondances de Galois.Bull. Soc. Math. Fr. 76 (1948), 114-155 French. Zbl 0033.00603, MR 0028814, 10.24033/bsmf.1401 |
| . |
