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Multialgebras, universal algebras and identities

Part of: Algebraic structures Other generalizations of groups

Published online by Cambridge University Press:  09 April 2009

Cosmin Pelea  and
Ioan Purdea
Cosmin Pelea
Affiliation:
“Babeş-Bolyai” University, Faculty of Mathematics and Computer Science, Cluj-Napoca, Romania, e-mail: cpelea@math.ubbcluj.ro, purdea@math.ubbcluj.ro
Ioan Purdea
Affiliation:
“Babeş-Bolyai” University, Faculty of Mathematics and Computer Science, Cluj-Napoca, Romania, e-mail: cpelea@math.ubbcluj.ro, purdea@math.ubbcluj.ro
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Abstract

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In this paper we determine the smallest equivalence relation on a multialgebra for which the factor multialgebra is a universal algebra satisfying a given identity. We also establish an important property for the factor multialgebra (of a multialgebra) modulo this relation.

Keywords

polynomial functionfactor multialgebraidentityhypergroupderived subhypergroup.

MSC classification

Secondary: 08A99: None of the above, but in this section 08A30: Subalgebras, congruence relations 20N20: Hypergroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 81 , Issue 1 , August 2006 , pp. 121 - 140
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Benado, M., ‘Les ensembles partiellement ordonnés et le théborème de raffinement de Schreier, II’, Czechoslovak Math. J. 5 (80) (1955), 308–344.CrossRefGoogle Scholar
[2]Breaz, S. and Pelea, C., ‘Multialgebras and term functions over the algebra of their nonvoid subsets’, Mathematica 43 (66) (2001), 143–149.Google Scholar
[3]Burris, S. and Sankappanavar, H. P., A course in universal algebra (Springer, New-York, 1981).CrossRefGoogle Scholar
[4]Corsini, P., Prolegomena of hypergroup theory, Supplement to Riv. Mat. Pura Appl. (Aviani Editore, Tricesimo, 1993).Google Scholar
[5]Corsini, P. and Leoreanu, V., Applications of hyperstructure theory (Kluwer, Boston, 2003).CrossRefGoogle Scholar
[6]Dresher, M. and Ore, O., ‘Theory of multigroups’, Amer. J. Math. 60 (1938), 705–733.CrossRefGoogle Scholar
[7]Freni, D., ‘A new characterization of the derived hypergroup via strongly regular equivalences’, Comm. Algebra 30 (2002), 3977–3989.CrossRefGoogle Scholar
[8]Grätzer, G., ‘A representation theorem for multi-algebras’, Arch. Math. 13 (1962), 452–456.CrossRefGoogle Scholar
[9]Grätzer, G., Universal algebra, 2nd edition (Springer, New York, 1979).CrossRefGoogle Scholar
[10]Pelea, C., ‘On the fundamental relation of a multialgebra’, Ital. J. Pure Appl. Math. 10 (2001), 141–146.Google Scholar
[11]Pelea, C., ‘Identities and multialgebras’, Ital. J. Pure Appl. Math. 15 (2004), 83–92.Google Scholar
[12]Pickett, H. E., ‘Homomorphisms and subalgebras of multialgebras’, Pacific J. Math. 21 (1967), 327–342.CrossRefGoogle Scholar
[13]Vougiouklis, T., ‘Representations of hypergroups by generalized permutations’, Algebra Universalis 29 (1992), 172–183.CrossRefGoogle Scholar
[14]Vougiouklis, T., ‘On Hv-rings and Hv-representations’, Discrete Math. 208/209 (1999), 615–620.CrossRefGoogle Scholar