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NEUTRAL ELEMENTS, FUNDAMENTAL RELATIONS AND n-ARY HYPERSEMIGROUPS.

Authors :
DAVVAZ, B.
DUDEK, W. A.
MIRVAKILI, S.
Source :
International Journal of Algebra & Computation. Jun2009, Vol. 19 Issue 4, p567-583. 17p.
Publication Year :
2009

Abstract

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. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
02181967
Volume :
19
Issue :
4
Database :
Academic Search Index
Journal :
International Journal of Algebra & Computation
Publication Type :
Academic Journal
Accession number :
41785052
Full Text :
https://doi.org/10.1142/S0218196709005226