American Journal of Modern Physics

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Santilli’s Isoprime Theory

Received: 02 June 2015    Accepted: 02 June 2015    Published: 11 August 2015
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Abstract

We study Santilli’s isomathematics for the generalization of modern mathematics via the isomultiplication a× ̂a=abT ̂ and isodivision a÷ ̂b=a/b I ̂, where the new multiplicative unit I ̂≠1 is called Santilli isounit, T ̂I ̂=1, and T ̂ is the inverse of the isounit, while keeping unchanged addition and subtraction, , In this paper, we introduce the isoaddition a+ ̂b=a+b+0 ̂ and the isosubtraction a- ̂b=a-b-0 ̂ where the additive unit 0 ̂≠0 is called isozero, and we study Santilli isomathem,atics formulated with the four isooperations (+ ̂,- ̂,× ̂,÷ ̂). We introduce, apparently for the first time, Santilli’s isoprime theory of the first kind and Santilli’s isoprime theory of the second kind. We also provide an example to illustrate the novel isoprime isonumbers

DOI 10.11648/j.ajmp.s.2015040501.12
Published in American Journal of Modern Physics (Volume 4, Issue 5-1, October 2015)

This article belongs to the Special Issue Issue I: Foundations of Hadronic Mathematics

Page(s) 17-23
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Isoprimes, Isomultiplication, Isodivision, Isoaddition, Isosubtraction

References
[1] R. M. Santilli, Isonumbers and genonumbers of dimension 1, 2, 4, 8, their isoduals and pseudoduals, and “hidden numbers” of dimension 3, 5, 6, 7, Algebras, Groups and Geometries 10, 273-322 (1993).
[2] Chun-Xuan Jiang, Foundations of Santilli’s isonumber theory, Part I: Isonumber theory of the first kind, Algebras, Groups and Geometries, 15, 351-393(1998).
[3] Chun-Xuan Jiang, Foundations of Santilli’s isonumber theory, Part II: Isonumber theory of the second kind, Algebras Groups and Geometries, 15, 509-544 (1998).
[4] Chun-Xuan Jiang, Foundations of Santilli’s isonumber theory. In: Foundamental open problems in sciences at the end of the millennium, T. Gill, K. Liu and E. Trell (Eds) Hadronic Press, USA, 105-139 (1999).
[5] Chun-Xuan Jiang, Foundations of Santilli’s isonumber theory, with applications to new cryptograms, Fermat’s theorem and Goldbach’s conjecture, International Academic Press, America- Europe- Asia (2002) (also available in the pdf file http: // www. i-b-r. org/jiang. Pdf)
[6] B. Green and T. Tao, The primes contain arbitrarily long arithmetic progressions, Ann. Math.,167,481-547(2008).
[7] E. Szemerédi, On sets of integers containing no elements in arithmetic progression, Acta Arith., 27, 299-345(1975).
[8] H. Furstenberg, Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions, J. Analyse Math., 31, 204-256 (1977).
[9] W. T. Gowers, A new proof of Szemerédi’s theorem, GAFA, 11, 465-588 (2001).
[10] B. Kra, The Green-Tao theorem on arithmetic progressions in the primes: an ergodic point of view, Bull. Amer. Math. Soc., 43, 3-23 (2006).
Author Information
  • Institute for Basic Research, Beijing, P. R. China

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  • APA Style

    Chun-Xuan Jiang. (2015). Santilli’s Isoprime Theory. American Journal of Modern Physics, 4(5-1), 17-23. https://doi.org/10.11648/j.ajmp.s.2015040501.12

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    Chun-Xuan Jiang. Santilli’s Isoprime Theory. Am. J. Mod. Phys. 2015, 4(5-1), 17-23. doi: 10.11648/j.ajmp.s.2015040501.12

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    Chun-Xuan Jiang. Santilli’s Isoprime Theory. Am J Mod Phys. 2015;4(5-1):17-23. doi: 10.11648/j.ajmp.s.2015040501.12

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  • @article{10.11648/j.ajmp.s.2015040501.12,
      author = {Chun-Xuan Jiang},
      title = {Santilli’s Isoprime Theory},
      journal = {American Journal of Modern Physics},
      volume = {4},
      number = {5-1},
      pages = {17-23},
      doi = {10.11648/j.ajmp.s.2015040501.12},
      url = {https://doi.org/10.11648/j.ajmp.s.2015040501.12},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajmp.s.2015040501.12},
      abstract = {We study Santilli’s isomathematics for the generalization of modern mathematics via the isomultiplication a× ̂a=abT ̂ and isodivision a÷ ̂b=a/b I ̂, where the new multiplicative unit I ̂≠1 is called Santilli isounit, T ̂I ̂=1, and T ̂ is the inverse of the isounit, while keeping unchanged addition and subtraction, , In this paper, we introduce the isoaddition a+ ̂b=a+b+0 ̂ and the isosubtraction a- ̂b=a-b-0 ̂ where the additive unit 0 ̂≠0 is called isozero, and we study Santilli isomathem,atics formulated with the four isooperations (+ ̂,- ̂,× ̂,÷ ̂). We introduce, apparently for the first time, Santilli’s isoprime theory of the first kind and Santilli’s isoprime theory of the second kind. We also provide an example to illustrate the novel isoprime isonumbers},
     year = {2015}
    }
    

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    AU  - Chun-Xuan Jiang
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    JF  - American Journal of Modern Physics
    JO  - American Journal of Modern Physics
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    AB  - We study Santilli’s isomathematics for the generalization of modern mathematics via the isomultiplication a× ̂a=abT ̂ and isodivision a÷ ̂b=a/b I ̂, where the new multiplicative unit I ̂≠1 is called Santilli isounit, T ̂I ̂=1, and T ̂ is the inverse of the isounit, while keeping unchanged addition and subtraction, , In this paper, we introduce the isoaddition a+ ̂b=a+b+0 ̂ and the isosubtraction a- ̂b=a-b-0 ̂ where the additive unit 0 ̂≠0 is called isozero, and we study Santilli isomathem,atics formulated with the four isooperations (+ ̂,- ̂,× ̂,÷ ̂). We introduce, apparently for the first time, Santilli’s isoprime theory of the first kind and Santilli’s isoprime theory of the second kind. We also provide an example to illustrate the novel isoprime isonumbers
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