Journal
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
Volume 19, Issue 4, Pages 567-583Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218196709005226
Keywords
n-ary operation; n-ary hyperoperation; n-ary hypersemigroup; fundamental equivalence relation
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The main tools in the theory of n-ary hyperstructures are the fundamental relations. The fundamental relation on an n-ary hypersemigroup is defined as the smallest equivalence relation so that the quotient would be the n-ary semigroup. In this paper we study neutral elements in n-ary hypersemigroups and introduce a new strongly compatible equivalence relation on an n-ary hypersemigroup so that the quotient is a commutative n-ary semigroup. Also we determine some necessary and sufficient conditions so that this relation is transitive. Finally, we prove that this relation is transitive on an n-ary hypergroup with neutral (identity) element.
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