Santilli’s Isoprime Theory

Received: 2 June 2015    Accepted: 2 June 2015    Published: 11 August 2015
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

Keywords

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).
• 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

ACS Style

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

AMA Style

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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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://article.sciencepublishinggroup.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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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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Author Information
• Institute for Basic Research, Beijing, P. R. China

• Sections