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In this paper, we introduce and explore suggested notions of `above', `below' and `between' in general groupoids, $Bin(X)$, as well as in more detail in several well-known classes of groupoids, including groups, semigroups, selective groupoids (digraphs), $d/BCK$-algebras, linear groupoids over fields and special cases, in order to illustrate the usefulness of these ideas. Additionally, for groupoid-classes (e.g., $BCK$-algebras) where these notions have already been accepted in a standard form, we look at connections between the several definitions which result from our introduction of these ideas as presented in this paper.
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참고문헌 (17)
참고문헌 신청
S. S. Ahn / 2014 / Neggers, Fuzzy upper bounds in groupoids / Sci. World J 2014:6
P. J. Allen / 2007 / Companion d-algebras / Math. Slovaca 57(2):93~106
P. J. Allen / 2016 / Several types of groupoids induced by two-variable functions / SpringerPlus 5(1):1715~1725
R. H. Bruck / 1971 / A Survey of Binary Systems / Springer
Hiba F. Fayoumi / 2011 / Locally-zero groupoids and the center of Bin(X) / 대한수학회논문집 26(2):163~168
P. J. Allen / 2007 / Companion d-algebras / Math. Slovaca 57(2):93~106
P. J. Allen / 2016 / Several types of groupoids induced by two-variable functions / SpringerPlus 5(1):1715~1725
R. H. Bruck / 1971 / A Survey of Binary Systems / Springer
Hiba F. Fayoumi / 2011 / Locally-zero groupoids and the center of Bin(X) / 대한수학회논문집 26(2):163~168
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