Bracket functions on groupoids
2
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
In this paper, we introduce an operation denoted by $[Br_e]$, a bracket operation, which maps an arbitrary groupoid $(X,*)$ on a set $X$ to another groupoid $(X,\bullet)=[Br_e](X,*)$ 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.
Abstract
In this paper, we introduce an operation denoted by $[Br_e]$, a bracket operation, which maps an arbitrary groupoid $(X,*)$ on a set $X$ to another groupoid $(X,\bullet)=[Br_e](X,*)$ 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.
참고문헌 (16)
- P. J. Allen, "Smarandache disjoint in BCK", d-algebras, 2005, pp.61(3), 447~449
- P. J. Allen, "Companion d-algebras", Math. Slovaca, 57(2), pp.93~106 (2007)
- Hiba F. Fayoumi, "Locally-zero groupoids and the center of Bin(X)", 대한수학회논문집, 26(2), pp.163~168 (2011), 대한수학회
- A. Iorgulescu, "Algebras of logic as BCK algebras" (2008), Editura ASE
- K. Iseki, "On BCI-algebras", Math. Sem. Notes Kobe Univ, 8(1), pp.125~130 (1980)
- K. Iseki, "An introduction to the theory of BCK-algebras", Math. Japon, 23(1), pp.1~26 (1978)
- Y. B. Jun, "Fuzzy d-ideals of d-algebras", J. Fuzzy Math, 8(1), pp.123~130 (2000)
- C. B. Kim, "Another axiomatization of B-algebras", Demonstratio Math, 41(2), pp.259~262 (2008)
- Hee Sik Kim, "The semigroups of binary systems and some perspectives", 대한수학회보, 45(4), pp.651~661 (2008), 대한수학회
- Y. C. Lee, "On dꠗ-subalgebras of d-transitive dꠗ-algebras", Math. Slovaca, 49(1), pp.27~33 (1999)
- J. Meng, "BCK-Algebras" (1994), Kyung Moon Sa
- J. Neggers, "On d-ideals in d-algebras", Math. Slovaca, 49(3), pp.243~251 (1999)
- J. Neggers, "On d-algebras", Math. Slovaca, 49(1), pp.19~26 (1999)
- J. Neggers, "On B-algebras", Mat. Vesnik, 54(1-2), pp.21~29 (2002)
- A. Walendziak, "Some axiomatizations of B-algebras", Math. Slovaca, 56(3), pp.301~306 (2006)
- H. Yisheng, BCI-Algebra, "Science Press" (2006), Science Press