Order related concepts for arbitrary groupoids
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
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.
Abstract
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.
참고문헌 (17)
- S. S. Ahn, "Neggers, Fuzzy upper bounds in groupoids", Sci. World J, 2014, pp.6~ (2014)
- P. J. Allen, "Companion d-algebras", Math. Slovaca, 57(2), pp.93~106 (2007)
- P. J. Allen, "Several types of groupoids induced by two-variable functions", SpringerPlus, 5(1), pp.1715~1725 (2016), Springer Nature[DOI]
- R. H. Bruck, "A Survey of Binary Systems" (1971), Springer
- Hiba F. Fayoumi, "Locally-zero groupoids and the center of Bin(X)", 대한수학회논문집, 26(2), pp.163~168 (2011), 대한수학회
- J. S. Han, "The hypergroupoid semigroups as generalizations of the groupoid semigroups", J. Appl. Math, 2012, pp.8~ (2012)
- Hee Sik Kim, "The semigroups of binary systems and some perspectives", 대한수학회보, 45(4), pp.651~661 (2008), 대한수학회
- J. Meng, "BCK-Algebras" (1994), Kyung Moon Sa
- J. Neggers, "Basic Poset" (1998), World Scientific
- J. Neggers, "On d-algebras", Math. Slovaca, 49(1), pp.19~26 (1999)
- S. J. Shin, "On Abelian and related fuzzy subsets of groupoids", Sci. World J, 2013, pp.5~ (2013)
- S. J. Shin, "The intersection between fuzzy subsets and groupoids", Sci. World J, 2014, pp.6~ (2014)
- S. Z. Song, "Soft saturated and dried values with applications in BCK", BCI-algebras, 2016, pp.21(3), 528~544
- R. Stanley, "Enumerative Combinatorics. Vol. 1", pp.1986, Wadsworth & Brooks
- D. B. West, "Introduction to Graph Theory" (2001), Prentice Hall
- H. Yisheng, "BCI-Algebra" (2006), Science Press
- J. Zhan, "On (fuzzy) weak-zero groupoids and (X,N)-zero groupoids", Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys, 78(2), pp.99~110 (2016)