Home Generalized Anti-Symmetry Laws in Groupoids
Article
Licensed
Unlicensed Requires Authentication

Generalized Anti-Symmetry Laws in Groupoids

  • Sun Shin Ahn , Hee Sik Kim and Young Joo Seo EMAIL logo
Published/Copyright: December 18, 2023
Become an author with De Gruyter Brill

ABSTRACT

In this paper, we introduce the notion of generalized anti-symmetry laws in groupoids, and we apply this concept to several algebraic structures. Moreover, we show that every Fibonacci sequence on (C, *) is periodic.

2020 Mathematics Subject Classification: Primary 20N02; 06F35

In memory of Professor Joseph Neggers

(Communicated by Anatolij Dvurečenskij)


REFERENCES

[1] Borůvka, O.: Foundations of the Ttheory of Groupoids and Groups, John Wiley & Sons, New York, 1976.10.1007/978-3-0348-4121-4Search in Google Scholar

[2] Bruck, R. H.: A Survey of Binary Systems, Springer, New York, 1971.10.1007/978-3-662-43119-1Search in Google Scholar

[3] Han, J. S.—Kim, H. S.—Neggers, J.: Strong and ordinary d-algebras, J. Mult.-Valued Log. Soft Comput. 16 (2010), 331–339.Search in Google Scholar

[4] Huang, Y.: BCI-Algebras, Science Press, Beijing, 2006.Search in Google Scholar

[5] Hwang, I. H.—Kim, H. S.—Neggers, J.: Some implicativities for groupoids and BCK-algebras, Mathematics 7 (2019), 973–800.10.3390/math7100973Search in Google Scholar

[6] Iorgulescu, A. Algebras of Logic as BCK-Algebras, Editura ASE, Bucharest, 2008.Search in Google Scholar

[7] Kim, H. S.—Neggers, J. The semigroups of binary systems and some perspectives, Bull. Korean Math. Soc. 45 (2008), 651–661.10.4134/BKMS.2008.45.4.651Search in Google Scholar

[8] Kim, H. S.—Neggers, J.—Ahn, S. S.: On pre-commutative algebras, Mathematics 7 (2019), 336–342.10.3390/math7040336Search in Google Scholar

[9] Liu, Y. L.—Kim, H. S.—Neggers, J.: Some special elements and pseudo inverse functions in groupoids, Mathematics 7 (2019), 173–179.10.3390/math7020173Search in Google Scholar

[10] Meng, J.—Jun, Y. B.: BCK-Algebras, Kyungmoon Sa, Seoul, 1994.Search in Google Scholar

[11] Neggers, J.—Kim, H. S.: On d-algebras, Math. Slovaca 49 (1999), 19–26.10.1023/A:1022416410366Search in Google Scholar

Received: 2022-11-15
Accepted: 2023-01-08
Published Online: 2023-12-18

© 2023 Mathematical Institute Slovak Academy of Sciences

Downloaded on 29.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/ms-2023-0104/html
Scroll to top button