{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T09:16:57Z","timestamp":1772270217728,"version":"3.50.1"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2009,6]]},"abstract":"<jats:p> 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. <\/jats:p>","DOI":"10.1142\/s0218196709005226","type":"journal-article","created":{"date-parts":[[2009,6,17]],"date-time":"2009-06-17T01:30:55Z","timestamp":1245202255000},"page":"567-583","source":"Crossref","is-referenced-by-count":39,"title":["NEUTRAL ELEMENTS, FUNDAMENTAL RELATIONS AND n-ARY HYPERSEMIGROUPS"],"prefix":"10.1142","volume":"19","author":[{"given":"B.","family":"DAVVAZ","sequence":"first","affiliation":[{"name":"Department of Mathematics, Yazd University, Yazd, Iran"}]},{"given":"W. A.","family":"DUDEK","sequence":"additional","affiliation":[{"name":"Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wyb. Wyspia\u0144skiego 27, 50-370 Wroclaw, Poland"}]},{"given":"S.","family":"MIRVAKILI","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Payame Noor University, Yazd, Iran"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","volume-title":"Prolegomena of Hypergroup Theory","author":"Corsini P.","year":"1993"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01243594"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/s000120050162"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3714-1"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2004.09.007"},{"key":"rf6","first-page":"165","volume":"30","author":"Davvaz B.","journal-title":"Iranian J. Sci. 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