Isorings and related isostructures

Raúl M. Falcón; Juan Núñez Valdés

Bollettino dell'Unione Matematica Italiana (2005)

  • Volume: 8-B, Issue: 2, page 437-452
  • ISSN: 0392-4041

Abstract

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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.

How to cite

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Falcón, Raúl M., and Núñez Valdés, Juan. "Isorings and related isostructures." Bollettino dell'Unione Matematica Italiana 8-B.2 (2005): 437-452. <http://eudml.org/doc/195414>.

@article{Falcón2005,
abstract = {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.},
author = {Falcón, Raúl M., Núñez Valdés, Juan},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {isotopic liftings of rings; quotient isorings; isoproducts; isoideals},
language = {eng},
month = {6},
number = {2},
pages = {437-452},
publisher = {Unione Matematica Italiana},
title = {Isorings and related isostructures},
url = {http://eudml.org/doc/195414},
volume = {8-B},
year = {2005},
}

TY - JOUR
AU - Falcón, Raúl M.
AU - Núñez Valdés, Juan
TI - Isorings and related isostructures
JO - Bollettino dell'Unione Matematica Italiana
DA - 2005/6//
PB - Unione Matematica Italiana
VL - 8-B
IS - 2
SP - 437
EP - 452
AB - 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.
LA - eng
KW - isotopic liftings of rings; quotient isorings; isoproducts; isoideals
UR - http://eudml.org/doc/195414
ER -

References

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  1. FALCÓN, R. M. - NÚÑEZ, J., Isogroups and Isosubgroups, Personal communication (Dpto de Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla (Spain)), 2002. Zbl1047.17511MR2036737
  2. JIANG, C. X., 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. Zbl0990.11059MR1975747
  3. KADEISVILI, J. V., Foundations of the Lie-Santilli isotheory, Rendiconti del Circolo Matematico di Palermo, 42, serie II (1996), 83-136. Zbl0889.53050MR1400884
  4. SANTILLI, R. M., 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. Zbl0428.70008MR510101
  5. SANTILLI, R. M., Isotopic liftings of contemporary mathematical structures, Hadronic Journal Suppl., 4 A (1988), 155-266. Zbl0755.70007MR1154654
  6. SANTILLI, R. M., 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. Zbl0755.70006MR1148906
  7. SANTILLI, R. M., 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. Zbl0806.19003MR1380794
  8. SANTILLI, R. M., Nonlocal-integral isotopies of differential calculus, mechanics and geometries, Rendicoti del Circolo Matematico di Palermo, 42, Serie II (1996), 7-82. Zbl0889.53049MR1400883
  9. SANTILLI, R. M., Relativistic Hadronic Mechanics: Nonunitary, Axiom-Preserving Completion of Relativistic Quantum Mechanics, Found. Phys., 2 7:5 (1997), 625-729. MR1459307
  10. SANTILLI, R. M., Isorepresentations of the Lie-isotopic SU(2) algebra with applications to Nuclear Physics and to Local Realism, Acta Appl. Math., 50 (1998), 177-190. Zbl0914.53040MR1608592
  11. SANTILLI, R. M., Physical Laws of new energies as predicted by hadronic mechanics, Journal New Energies Papers I, II, III, IV and V (1999), in press. 
  12. SANTILLI, R. M. - SHILLADY, D. D., A new isochemical model of the water molecule, Intern. J. Hydrogen Energy, 25 (2000), 173-183. 
  13. TSAGAS, G. T. - SOURLAS, D. S., Mathematical Foundations of the Lie-Santilli Theory, Hadronic Press (1993). Zbl0895.53003MR1261870

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