η-Relations and Transitivity Conditions of η on Hyper-MV Algebras
S. Rasouli, D. Heidari and B. Davvaz
In this paper, we consider the notion of a hyper-MV algebra, we give some examples and we introduce the relation η, then we consider the transitive closure of η. In a hyper-MV algebra, the fundamental relation is defined as the smallest equivalence relation so that the quotient is the (fundamental) MV-algebra. We show that η* is the fundamental relation in a hyper-MV algebra. Finally, we find equivalent conditions with the transitivity of the relation η.
Keywords: Hyper-MV algebra, strongly regular relation, fundamental relation.
2000 Mathematics Subject Classification: 06D35, 20N20.