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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.
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참고문헌 (16)
참고문헌 신청
P. J. Allen / 2005 / Smarandache disjoint in BCK/d-algebras / Sci. Math. Jpn 61(3):447~449
P. J. Allen / 2007 / Companion d-algebras / Math. Slovaca 57(2):93~106
Hiba F. Fayoumi / 2011 / Locally-zero groupoids and the center of Bin(X) / 대한수학회논문집 26(2):163~168
A. Iorgulescu / 2008 / Algebras of logic as BCK algebras / Editura ASE
K. Iseki / 1980 / On BCI-algebras / Math. Sem. Notes Kobe Univ 8(1):125~130
P. J. Allen / 2007 / Companion d-algebras / Math. Slovaca 57(2):93~106
Hiba F. Fayoumi / 2011 / Locally-zero groupoids and the center of Bin(X) / 대한수학회논문집 26(2):163~168
A. Iorgulescu / 2008 / Algebras of logic as BCK algebras / Editura ASE
K. Iseki / 1980 / On BCI-algebras / Math. Sem. Notes Kobe Univ 8(1):125~130
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