PROPERTIES OF HYPERPRODUCTS AND THE RELATION β IN QUASIHYPERGROUPS
Some properties of the complete parts in hyper-groupoids are established. Applying these properties to the case of quasihypergroups H for which H/β*. is a quasigroup, a necessary and sufficient condition for the transitivity of the relation β is proved. Consequently, several classes of quasihypergro...
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| Format: | Article |
| Language: | English |
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Accademia Piceno Aprutina dei Velati
1997-02-01
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| Series: | Ratio Mathematica |
| Online Access: | http://eiris.it/ojs/index.php/ratiomathematica/article/view/116 |
| Summary: | Some properties of the complete parts in hyper-groupoids are established. Applying these properties to the case of quasihypergroups H for which H/β*. is a quasigroup, a necessary and sufficient condition for the transitivity of the relation β is proved. Consequently, several classes of quasihypergroups in which β is transitive are obtained (for instance, in any finite quasihypergroup with identity β is a transitive relation). Then, in the case of quasihypergroups having underlying groups, the relation β is completely de-termined. |
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| ISSN: | 1592-7415 2282-8214 |