Geodesic
Isorings and related isostructures
Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 2, pp. 437-452.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

The main goal of this paper is to give a mathematical foundation, serious and consistent, to some parts of Santilli’s isotheory. We study the isotopic liftings of rings, subrings and ideals, and we also introduce the concept of quotient isoring. By using the isoproduct model, necessary conditions assuring the existence of such isostructures are given. Such conditions are based on the inner laws which originate the associated elements of isotopy. These elements will allow to extend, from a different point of view, the Santilli’s study of non-linear generalized theory. Several examples of these isostructures are also shown. We finally find the differences between a quotient isoring and a quotient ring coming from an isoring and one of its isoideals.
Lo scopo principale di questo articolo è dare una fondazione matematica, seria e costante a delle parti dell'isoteoria di Santilli. Noi studiamo i sollevamenti isotopici di anelli, sottoanelli ed ideali. Usando il modello della isomoltiplicazione, condizioni necessarie che assicurano l'esistenza di tali isostrutture sono date. Tali condizioni sono basate sulle leggi interne che originano gli elementi associati di sollevamenti isotopici. Questi elementi permetteranno di estendere, da un punto di vista diverso lo studio di Santilli di teoria generalizzata e non-lineare. Molti esempi di queste isostrutture sono dati. Noi troviamo infine le differenze tra un isoanello quoziente ed un anello quoziente provenienti da un isoanello e da uno dei suoi isoideali. 
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Falcón, Raúl M.; Núñez Valdés, Juan. Isorings and related isostructures. Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 2, pp. 437-452. http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_2_a10/

[1] R. M. Falcón - J. Núñez , Isogroups and Isosubgroups, Personal communication (Dpto de Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla (Spain)), 2002. | MR | Zbl

[2] C. X. Jiang , Foundations of Santilli's isonumber Theory with applications to New Cryptograms, Fermat's Theorem and Goldbach's Conjecture, International Academic Press, American-Europe-Asia, 2002. | MR | Zbl

[3] J. V. Kadeisvili , Foundations of the Lie-Santilli isotheory, Rendiconti del Circolo Matematico di Palermo, 42, serie II (1996), 83-136. | MR | Zbl

[4] R. M. Santilli , On a possible Lie-admissible covering of the Galilei Relativity in Newtonian Mechanics for nonconservative and Galilei noninvariant systems, Hadronic Journal, 1 (1978), 223-423. Addendum, ibid, 1 (1978), 1279-1342. | MR | Zbl

[5] R. M. Santilli , Isotopic liftings of contemporary mathematical structures, Hadronic Journal Suppl., 4 A (1988), 155-266. | MR | Zbl

[6] R. M. Santilli , Isotopies of contemporary mathematical structures, I: Isotopies of fields, vector spaces, transformation theory, Lie algebras, analytic mechanics and space-time symmetries, Algebras, Groups and Geometries, 8 (1991), 169-266. | MR | Zbl

[7] R. M. Santilli , Isonumbers and genonumbers of dimension 1, 2, 4, 8, their isoduals and pseudoisoduals, and hidden numbers of dimension 3, 5, 6, 7, Algebras, Groups and Geometries (1993), 273-322. | MR | Zbl

[8] R. M. Santilli , Nonlocal-integral isotopies of differential calculus, mechanics and geometries, Rendicoti del Circolo Matematico di Palermo, 42, Serie II (1996), 7-82. | MR | Zbl

[9] R. M. Santilli , Relativistic Hadronic Mechanics: Nonunitary, Axiom-Preserving Completion of Relativistic Quantum Mechanics, Found. Phys., 2 7:5 (1997), 625-729. | MR

[10] R. M. Santilli , Isorepresentations of the Lie-isotopic SU(2) algebra with applications to Nuclear Physics and to Local Realism, Acta Appl. Math., 50 (1998), 177-190. | MR | Zbl

[11] R. M. Santilli , Physical Laws of new energies as predicted by hadronic mechanics, Journal New Energies Papers I, II, III, IV and V (1999), in press.

[12] R. M. Santilli - D. D. Shillady , A new isochemical model of the water molecule, Intern. J. Hydrogen Energy, 25 (2000), 173-183.

[13] G. T. Tsagas - D. S. Sourlas , Mathematical Foundations of the Lie-Santilli Theory, Hadronic Press (1993). | MR | Zbl