LOCALLY-ZERO GROUPOIDS AND THE CENTER OF BIN(X)

Title & Authors
LOCALLY-ZERO GROUPOIDS AND THE CENTER OF BIN(X)
Fayoumi, Hiba F.;

Abstract
In this paper we introduce the notion of the center ZBin(X) in the semigroup Bin(X) of all binary systems on a set X, and show that if (X,$\small{{\bullet}}$) $\small{{\in}}$ ZBin(X), then x $\small{{\neq}}$ y implies {x,y}=$\small{{x{\bullet}y,y{\bullet}x}}$. Moreover, we show that a groupoid (X,$\small{{\bullet}}$) $\small{{\in}}$ ZBin(X) if and only if it is a locally-zero groupoid.
Keywords
center;locally-zero;Bin(X);
Language
English
Cited by
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The Interaction between Fuzzy Subsets and Groupoids, The Scientific World Journal, 2014, 2014, 1
2.
Hyperfuzzy subsets and subgroupoids, Journal of Intelligent & Fuzzy Systems, 2017, 33, 3, 1553
3.
Fuzzy rank functions in the set of all binary systems, SpringerPlus, 2016, 5, 1
4.
The Hypergroupoid Semigroups as Generalizations of the Groupoid Semigroups, Journal of Applied Mathematics, 2012, 2012, 1
5.
On Abelian and Related Fuzzy Subsets of Groupoids, The Scientific World Journal, 2013, 2013, 1
6.
Fuzzy Upper Bounds in Groupoids, The Scientific World Journal, 2014, 2014, 1
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