Using Divisor Function and Euler Product Function in Abstract Algebra Concepts

K. Subbanna; S. Venkatarami Reddy; S. Gouse Mohiddin; R. Bhuvana Vijaya

doi:doi:10.11648/j.ijtam.20190504.11

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Using Divisor Function and Euler Product Function in Abstract Algebra Concepts

K. Subbanna, S. Venkatarami Reddy, S. Gouse Mohiddin, R. Bhuvana Vijaya

Published in International Journal of Theoretical and Applied Mathematics (Volume 5, Issue 4)

Received: 10 August 2019 Accepted: 19 September 2019 Published: 9 October 2019

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Abstract

Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers, finite fields, and function fields. These properties, such as whether a ring admits unique factorization, the behavior of ideals, and the Galois groups of fields, can resolve questions of primary importance in number theory. In this paper for the most part centered around number theory ideas which are utilized in different themes like group theory and ring theory, these speculations are extremely unique ideas to comprehend among this we might want to express our perspectives as far as number hypothesis/theory ideas, such as, to calculate some subgroups of a cyclic group, number of ideals, principal ideals of a ring and number of generators of a cyclic group as far as both regular procedure and number speculation/hypothesis thoughts.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 5, Issue 4)
DOI	10.11648/j.ijtam.20190504.11
Page(s)	57-62
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), 2019. Published by Science Publishing Group

Keywords

Divisors Function, Euler's Phi-function, Field, Number Theory, Abstract Algebra

References

[1]	W. W. Adams and L. J. Goldstein, Introduction to Number Theory, Prentice-Hall, Englewood Cliffs, New Jersey, 1g76.
[2]	G. E. Andrews, Number Theory, w. B. Saunders, Philadelphia, lg7l.
[3]	T. A. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976.
[4]	R' G. Archibald, an Introduction to the Theory of Numbers, Merrill, Columbus, Ohio, 1970.
[5]	N. S. Gopalakrishnan, University algebra, Second edition, New Age International (P) limited, publishers.
[6]	Kratzel E., Lattice points, Kluwer Academic Publishers, 1988.
[7]	Petermann Y.-F. S. and Wu Jie, on the sum of the exponential divisors of an integer, Acta Math. Hungar., 77 (1997), 159-175.
[8]	Pillai S. S., On an arithmetic function, Journ. Annamalai Univ., 2 (1933), 243-248.
[9]	Subbarao M. V., on some arithmetical convolutions, the theory of arithmetical functions, Lecture Notes in Mathematics 251, Springer Verlag, 1972, 247-271.
[10]	Toth L., On certain arithmetical functions involving exponential divisors, Annales Univ. Sci. Budapest. Sect. Comp., 24 (2004), 285-294.
[11]	Toth L., on certain arithmetical functions involving exponential divisors Annales Univ. Sci. Budapest. Sect. Comp., 27 (2007), 155-166.
[12]	D. S. Dummit and R. M. Foote, Abstract algebra, third edition. John Wiley & Sons, Inc., Hoboken, NJ, 2004.
[13]	C. F. Gauss, Untersuchungen ¨Uber Hohere Arithmetik, second edition, reprinted, Chelsea publishing company, New York 1981.
[14]	K. Ireland and M. Rosen, A classical introduction to modern number theory, second edition, Springer-Verlag, GTM Vol 84 (second edition) 1990.
[15]	T. W. Judson, Abstract Algebra: Theory and Applications, PWS-Kent, Boston, 1994.
[16]	Daniel Marcus, Number Fields.
[17]	Serge Lang, Algebraic Number Fields.
[18]	Pierre Samuel, Algebraic Theory of Numbers.
[19]	Gerald Janusz, Algebraic Number Fields.

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APA Style

K. Subbanna, S. Venkatarami Reddy, S. Gouse Mohiddin, R. Bhuvana Vijaya. (2019). Using Divisor Function and Euler Product Function in Abstract Algebra Concepts. International Journal of Theoretical and Applied Mathematics, 5(4), 57-62. https://doi.org/10.11648/j.ijtam.20190504.11

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ACS Style

K. Subbanna; S. Venkatarami Reddy; S. Gouse Mohiddin; R. Bhuvana Vijaya. Using Divisor Function and Euler Product Function in Abstract Algebra Concepts. Int. J. Theor. Appl. Math. 2019, 5(4), 57-62. doi: 10.11648/j.ijtam.20190504.11

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AMA Style

K. Subbanna, S. Venkatarami Reddy, S. Gouse Mohiddin, R. Bhuvana Vijaya. Using Divisor Function and Euler Product Function in Abstract Algebra Concepts. Int J Theor Appl Math. 2019;5(4):57-62. doi: 10.11648/j.ijtam.20190504.11

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@article{10.11648/j.ijtam.20190504.11,
  author = {K. Subbanna and S. Venkatarami Reddy and S. Gouse Mohiddin and R. Bhuvana Vijaya},
  title = {Using Divisor Function and Euler Product Function in Abstract Algebra Concepts},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {5},
  number = {4},
  pages = {57-62},
  doi = {10.11648/j.ijtam.20190504.11},
  url = {https://doi.org/10.11648/j.ijtam.20190504.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20190504.11},
  abstract = {Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers, finite fields, and function fields. These properties, such as whether a ring admits unique factorization, the behavior of ideals, and the Galois groups of fields, can resolve questions of primary importance in number theory. In this paper for the most part centered around number theory ideas which are utilized in different themes like group theory and ring theory, these speculations are extremely unique ideas to comprehend among this we might want to express our perspectives as far as number hypothesis/theory ideas, such as, to calculate some subgroups of a cyclic group, number of ideals, principal ideals of a ring and number of generators of a cyclic group as far as both regular procedure and number speculation/hypothesis thoughts.},
 year = {2019}
}

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TY  - JOUR
T1  - Using Divisor Function and Euler Product Function in Abstract Algebra Concepts
AU  - K. Subbanna
AU  - S. Venkatarami Reddy
AU  - S. Gouse Mohiddin
AU  - R. Bhuvana Vijaya
Y1  - 2019/10/09
PY  - 2019
N1  - https://doi.org/10.11648/j.ijtam.20190504.11
DO  - 10.11648/j.ijtam.20190504.11
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 57
EP  - 62
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20190504.11
AB  - Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers, finite fields, and function fields. These properties, such as whether a ring admits unique factorization, the behavior of ideals, and the Galois groups of fields, can resolve questions of primary importance in number theory. In this paper for the most part centered around number theory ideas which are utilized in different themes like group theory and ring theory, these speculations are extremely unique ideas to comprehend among this we might want to express our perspectives as far as number hypothesis/theory ideas, such as, to calculate some subgroups of a cyclic group, number of ideals, principal ideals of a ring and number of generators of a cyclic group as far as both regular procedure and number speculation/hypothesis thoughts.
VL  - 5
IS  - 4
ER  -

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Author Information

K. Subbanna

Department of Mathematics, Besant Theosophical College, Madanapalle Andhra Pradesh, India
S. Venkatarami Reddy

Department of Mathematics, Besant Theosophical College, Madanapalle Andhra Pradesh, India
S. Gouse Mohiddin

Department of Mathematics, Madanapalle Institute of Technology & Science, Madanapalle, Andhra Pradesh, India
R. Bhuvana Vijaya

Department of Mathematics, Jntua College of Engineering Anantapur, Anantapuramu, Andhra Pradesh, India

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Plain Text BibTeX RIS

APA Style

K. Subbanna, S. Venkatarami Reddy, S. Gouse Mohiddin, R. Bhuvana Vijaya. (2019). Using Divisor Function and Euler Product Function in Abstract Algebra Concepts. International Journal of Theoretical and Applied Mathematics, 5(4), 57-62. https://doi.org/10.11648/j.ijtam.20190504.11

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ACS Style

K. Subbanna; S. Venkatarami Reddy; S. Gouse Mohiddin; R. Bhuvana Vijaya. Using Divisor Function and Euler Product Function in Abstract Algebra Concepts. Int. J. Theor. Appl. Math. 2019, 5(4), 57-62. doi: 10.11648/j.ijtam.20190504.11

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AMA Style

K. Subbanna, S. Venkatarami Reddy, S. Gouse Mohiddin, R. Bhuvana Vijaya. Using Divisor Function and Euler Product Function in Abstract Algebra Concepts. Int J Theor Appl Math. 2019;5(4):57-62. doi: 10.11648/j.ijtam.20190504.11

Copy | Download

@article{10.11648/j.ijtam.20190504.11,
  author = {K. Subbanna and S. Venkatarami Reddy and S. Gouse Mohiddin and R. Bhuvana Vijaya},
  title = {Using Divisor Function and Euler Product Function in Abstract Algebra Concepts},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {5},
  number = {4},
  pages = {57-62},
  doi = {10.11648/j.ijtam.20190504.11},
  url = {https://doi.org/10.11648/j.ijtam.20190504.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20190504.11},
  abstract = {Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers, finite fields, and function fields. These properties, such as whether a ring admits unique factorization, the behavior of ideals, and the Galois groups of fields, can resolve questions of primary importance in number theory. In this paper for the most part centered around number theory ideas which are utilized in different themes like group theory and ring theory, these speculations are extremely unique ideas to comprehend among this we might want to express our perspectives as far as number hypothesis/theory ideas, such as, to calculate some subgroups of a cyclic group, number of ideals, principal ideals of a ring and number of generators of a cyclic group as far as both regular procedure and number speculation/hypothesis thoughts.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Using Divisor Function and Euler Product Function in Abstract Algebra Concepts
AU  - K. Subbanna
AU  - S. Venkatarami Reddy
AU  - S. Gouse Mohiddin
AU  - R. Bhuvana Vijaya
Y1  - 2019/10/09
PY  - 2019
N1  - https://doi.org/10.11648/j.ijtam.20190504.11
DO  - 10.11648/j.ijtam.20190504.11
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 57
EP  - 62
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20190504.11
AB  - Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers, finite fields, and function fields. These properties, such as whether a ring admits unique factorization, the behavior of ideals, and the Galois groups of fields, can resolve questions of primary importance in number theory. In this paper for the most part centered around number theory ideas which are utilized in different themes like group theory and ring theory, these speculations are extremely unique ideas to comprehend among this we might want to express our perspectives as far as number hypothesis/theory ideas, such as, to calculate some subgroups of a cyclic group, number of ideals, principal ideals of a ring and number of generators of a cyclic group as far as both regular procedure and number speculation/hypothesis thoughts.
VL  - 5
IS  - 4
ER  -

Copy | Download