Independence concepts for groupoids

Authors

  • Akbar Rezaei Department of Mathematics, Payame Noor University, Teheran
  • Hee Sik Kim Research Institute for Natural Sci., Department of Mathematics, Hanyang University, Seoul
  • Arsham Borumand Saeid Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman

Keywords:

groupoid, (right, left) independent, strongly (right, left) independent, dynamic

Abstract

In this paper, for getting more results in groupoids, we consider a set and introduce the notion of a right (left) independent subset of a groupoid, and it is studied in detail. As a corollary of these properties, the following important result is proved: for any groupoid, there is a maximal right (left) independent subset.

References

Allen, Paul J., Hee Sik Kim, and Joseph Neggers. Several types of groupoids induced by two-variables functions," Springer Plus 5 (2016): Art. no. 1715.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Bruck, Richard Hubert. A Survey of Binary Systems. Vol. 20 of Ergebnisse der Mathematik und Ihrer Grenzgebiete. 1. Folge. Springer: New York, 1971.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Boruvka, Otakar. Foundations of the Theory of Groupoids and Groups. Springer Basel AG: Berlin, 1976.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Chajda, Ivan, and Helmut Länger. "Groupoids assigned to relational systems." Math. Bohem. 138, no. 1 (2013): 15–23.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Chajda, Ivan, Helmut Länger. "Groupoids corresponding to relational systems". Miskolc Math. Notes 17, no. 1 (2016): 111-118.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Fayoumi, Hiba Farouk. "Locally-Zero groupoids and the center of Bin(X)". Commun. Korean Math. Soc. 26, no. 2 (2011): 163-168.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Fayoumi, Hiba Farouk. "Groupoid factorizations in the semigroup of binary systems". Sci. Math. Japo. (to appear).
##plugins.generic.googleScholarLinks.settings.viewInGS##

Feng, Feng, Hee Sik Kim, and Joseph Neggers. "General implicativity in groupoids". Mathematics 6, no. 11 (2018): Art. no. 235.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Huang, Yisheng. BCI-Algebra Beijing: Science Press, 2006.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Hwang, In Ho, Hee Sik Kim, and Joseph Neggers. "Locally finiteness and convolution products in groupoids." AIMS Math. 5, no. 6 (2020): 7350-7358.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Iorgulescu, Afrodita. Algebras of Logic as BCK-algebras. Bucharest: Editura ASE, 2008.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Kim, Jong Youl, Young Bae Jun, and Hee Sik Kim. "BCK-algebras inherited from the posets." Math. Japo. 45, no. 1 (1997): 119-123.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Kim, Young Hee, Hee Sik Kim, and Joseph Neggers. "Selective groupoids and frameworks induced by fuzzy subsets." Iran. J. Fuzzy Syst. 14, no. 3 (2017): 151-160.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Kim, Hee Sik, and Joseph Neggers. "The semigroups of binary systems and some perspectives." Bull. Korean Math. Soc. 45, no. 4 (2008): 651-661.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Liu, Yong Lina, Hee Sik Kim, and Joseph Neggers. "Hyperfuzzy subsets and subgroupoids." J. Intell. Fuzzy Syst. 33, no. 3 (2017): 1553-1562.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Meng, Jie, and Young Bae Jun. BCK-algebras. Seoul: Kyung Moon Sa Company, 1994
##plugins.generic.googleScholarLinks.settings.viewInGS##

Nebeský, Ladislav. "Travel groupoids." Czechoslovak Math. 56(131), no. 2 (2006): 659-675.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Neggers, Joseph, and Hee Sik Kim. "On d-algebras." Math. Slovaca 49, no. 1 (1999): 19-26.
##plugins.generic.googleScholarLinks.settings.viewInGS##

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Published

2023-07-18

How to Cite

Rezaei, A., Kim, H. S., & Saeid, A. B. (2023). Independence concepts for groupoids. Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica, 22, 87–98. Retrieved from https://studmath.uken.krakow.pl/article/view/10432

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