2016-Sustainable Industrial Processing Summit
SIPS 2016 Volume 4: Santilli Intl. Symp. / Mathematics Applications
| Editors: | Kongoli F, Gaines G, Georgiev S, Bhalekar A |
| Publisher: | Flogen Star OUTREACH |
| Publication Year: | 2016 |
| Pages: | 320 pages |
| ISBN: | 978-1-987820-42-3 |
| ISSN: | 2291-1227 (Metals and Materials Processing in a Clean Environment Series) |
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Helix-Hopes On Finite Hv-Fields
Thomas Vougiouklis1; Sousana Vougiouklis2;1DEMOCRITUS UNIVERSITY OF THRACE, Xanthi, Greece; 2MUSICIAN, Athens, Greece;
Type of Paper: Regular
Id Paper: 441
Topic: 38
Abstract:
Our main object is the class of hyperstructures called Hv-structures introduced in 1990 [4], which satisfy the weak axioms where the non-empty intersection replaces the equality.
Algebraic hyperstructure is called a set H equipped with at least one hyperoperation (abbreviation: hyperoperation=hope): :HHP(H)-{}. Abbreviate by WASS the weak associativity: (xy)zx(yz), x,y,zH and by COW the weak commutativity: xyyx, x,yH. The hyperstructure (H,) is called Hv-semigroup if it is WASS, it is called Hv-group if it is reproductive Hv-semigroup.
The main tools of this theory are the fundamental relations which connect the Hv-structures with the corresponding classical ones. The fundamental relations are used to define more complicated hyperstructures as Hv-fields, Hv-vector spaces and so on, as well.
Since the class of Hv-structures is extremely large, we can define new hyperoperations and we can apply them in mathematics and in applied sciences, as in the Santilli’s iso-theory, as well. A new hyperoperation is the so-called helix-hope. We present here this theory and focus on finite Hv-fields.