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NEUTRAL ELEMENTS, FUNDAMENTAL RELATIONS AND n-ARY HYPERSEMIGROUPS.
- 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]
- Subjects :
- *SEMIGROUPS (Algebra)
*SET theory
*MONOIDS
*MATHEMATICS
*ARITHMETIC
Subjects
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