[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c180136

BRACKET FUNCTIONS ON GROUPOIDS

Allen, Paul J. (Department of Mathematics University of Alabama)
Kim, Hee Sik (Research Institute for Natural Sci. Department of Mathematics Hanyang University)
Neggers, Joseph (Department of Mathematics University of Alabama)

Publication Information

Communications of the Korean Mathematical Society / v.34, no.2, 2019 , pp. 375-381 More about this Journal

Abstract

In this paper, we introduce an operation denoted by [ $Br_e$ ], a bracket operation, which maps an arbitrary groupoid ( $X,{\ast}$ ) on a set X to another groupoid $$(X,{\bullet})=[Br_e$ $]$ $(X,{\ast})$$ which on groups corresponds to sending a pair of elements (x, y) of X to its commutator $xyx^{-1}y^{-1}$ . When applied to classes such as d-algebras, BCK-algebras, a variety of results is obtained indicating that this construction is more generally useful than merely for groups where it is of fundamental importance.

Keywords

bracket function; e-bracket image algebra; e-bracket-abelian; d/B/BCK-algebra; Smarandache disjoint; Bin(X);

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

Reference
Cited By KSCI

1	Y. C. Lee and H. S. Kim, On d-subalgebras of d-transitive d-algebras, Math. Slovaca 49 (1999), no. 1, 27-33.
2	J. Meng and Y. B. Jun, BCK-Algebras, Kyung Moon Sa, Seoul, 1994.
3	J. Neggers, Y. B. Jun, and H. S. Kim, On d-ideals in d-algebras, Math. Slovaca 49 (1999), no. 3, 243-251.
4	J. Neggers and H. S. Kim, On d-algebras, Math. Slovaca 49 (1999), no. 1, 19-26.
5	J. Neggers and H. S. Kim, On B-algebras, Mat. Vesnik 54 (2002), no. 1-2, 21-29.
6	A. Walendziak, Some axiomatizations of B-algebras, Math. Slovaca 56 (2006), no. 3, 301-306.
7	H. Yisheng, BCI-Algebra, Science Press, Beijing, 2006.
8	H. F. Fayoumi, Locally-zero groupoids and the center of Bin(X), Commun. Korean Math. Soc. 26 (2011), no. 2, 163-168. DOI
9	P. J. Allen, H. S. Kim, and J. Neggers, Smarandache disjoint in BCK/d-algebras, Sci. Math. Jpn. 61 (2005), no. 3, 447-449.
10	P. J. Allen, H. S. Kim, and J. Neggers, Companion d-algebras, Math. Slovaca 57 (2007), no. 2, 93-106. DOI
11	A. Iorgulescu, Algebras of logic as BCK algebras, Editura ASE, Bucharest, 2008.
12	K. Iseki, On BCI-algebras, Math. Sem. Notes Kobe Univ. 8 (1980), no. 1, 125-130.
13	K. Iseki and S. Tanaka, An introduction to the theory of BCK-algebras, Math. Japon. 23 (1978/79), no. 1, 1-26.
14	Y. B. Jun, J. Neggers, and H. S. Kim, Fuzzy d-ideals of d-algebras, J. Fuzzy Math. 8 (2000), no. 1, 123-130.
15	C. B. Kim and H. S. Kim, Another axiomatization of B-algebras, Demonstratio Math. 41 (2008), no. 2, 259-262. DOI
16	H. S. Kim and J. Neggers, The semigroups of binary systems and some perspectives, Bull. Korean Math. Soc. 45 (2008), no. 4, 651-661. DOI