Birth of Compound Numbers

Ranjit Biswas^1,

¹Department of Computer Science, Jamia Hamdard University, Hamdard Nagar, New Delhi, INDIA

Cite this paper:
Ranjit Biswas. Birth of Compound Numbers. Turkish Journal of Analysis and Number Theory. 2014; 2(6):208-219. doi: 10.12691/tjant-2-6-4

Abstract

In this paper the author introduces a new kind of numbers called by ‘Compound Numbers’. A region R may or may not have imaginary object. A region even may have more than one imaginary objects too. Corresponding to an imaginary object (if exists) of a region R, we get compound objects for the region R. Imaginary objects and compound objects of a region R are not members of R and so they are called imaginary with respect to the region R only (i.e. it is a local characteristics property with respect to the region concerned), as they could be core members of another region. Every region has its own set of imaginary numbers (if exist). As a particular instance, the compound objects of the set of real numbers are the complex numbers (of existing concept). In this paper the author discovers imaginary objects of the region C (the set of complex numbers). The compound objects of C are called by ‘compound numbers’. Collection of all compound numbers is denoted by the set E. This work just reports the birth of compound numbers, not further details at this stage. It is claimed that “Theory of Numbers” will get a new direction by the birth of compound numbers. A new “Theory of Objects’ and the classical “Theory of Numbers” as a special case of it were also studied in . In this paper we say that every complete region has its own ‘Theory of Numbers’, where the classical ‘theory of numbers’ is just a special instance corresponding to a particular complete region RR. Consequently, we also introduce a new field called by “Object Geometry” of a complete region, being a generalization of our classical geometry of the existing style, from elementary to the higher level.

Keywords:
region im-object im-number rim cim compound object compound number onteger

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	Alperin, J. L., with R. B. Bell, Groups and Representations, Graduate Texts in Mathematics, Vol. 162, Springer-Verlag, New York, 1995.
[2]	Artin, Michael, Algebra, Prentice Hall, New York, 1991.
[3]	Beachy, J. A., and W. D. Blair, Abstract Algebra, 2nd Ed., Waveland Press, Prospect Heights, Ill., 1996.
[4]	Bourbaki, Nicolas, Elements of Mathematics: Algebra I, New York: , 1998.
[5]	Dixon, G.M., Division Algebras: Octonions Quaternions Complex Numbers and the Algebraic Design of Physics, December 2010, Kluwer Academic Publishers, Dordrecht.
[6]	Ellis, G., Rings and Fields, Oxford University Press, 1993.
[7]	Hideyuki Matsumura, Commutative Ring Theory, Cambridge University Press, Cambridge, 1986
[8]	Hungerford, T., Algebra, Graduate Texts in Mathematics, Vol. 73, Springer-Verlag, New York, 1974.
[9]	I. N. Herstein, Topics in Algebra, Wiley Eastern Limited, New Delhi, 2001.
[10]	Jacobson, N., Basic Algebra I, 2nd Ed., W. H. Freeman & Company Publishers, San Francisco, 1985.
[11]	Jacobson, N., Basic Algebra II, 2nd Ed., W. H. Freeman & Company Publishers, San Francisco, 1989.
[12]	Lam, T. Y., Exercises in Classical Ring Theory, Problem Books in Mathematics, Springer-Verlag, New York, 1995.
[13]	Lang, Serge, Undergraduate Algebra (3rd ed.), Berlin, New York: , 2005.
[14]	Nathan Jacobson, The Theory of Rings. American Mathematical Society Mathematical Surveys, Vol. I. American Mathematical Society, New York, 1943.
[15]	Pierce, Richard S., Associative algebras. Graduate Texts in Mathematics, 88. Studies in the History of Modern Science, 9. Springer-Verlag, New York-Berlin, 1982.
[16]	Ranjit Biswas, Region Algebra, Theory of Objects & Theory of Numbers, International Journal of Algebra, Vol. 6 (28) 2012 page 1371-1417.
[17]	Ranjit Biswas, Calculus Space, International Journal of Algebra, Vol. 7, 2013, No.16, 791-801.
[18]	Van der Waerden, B. L., Algebra, Springer-Verlag, New York, 1991.
[19]	Van der Waerden, Bartel Leendert, Algebra, Berlin, New York: , 1993, ISBN 978-3-540-56799-8.
[20]	Walter Rudin, Real and Complex Analysis, McGraw Hills Education, India, August’ 2006.