Irreducibility of A Formal Power Series with Integer Coefficients

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Authors

  • Mriganka S. Dutta
     Department of Mathematics, Nalbari College, Nalbari 781335 ,IN
  • Helen K. Saikia
     Department of Mathematics, Gauhati University, Guwahati 781014 ,IN

DOI:

https://doi.org/10.18311/jims/2021/24897

Keywords:

Irreducible element, invertible element, factorization, formal power series ring
13P05, 13F25, 11Y05

Abstract

In this article, we have established a relation between total number of partitions of a positive integer n and all possible factorizations of a power series with constant term prime power pn, into irreducible power series. Finally we try to develop an irreducibility criterion for power series whose constant term is a prime power.

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Published

2021-06-14

How to Cite

Dutta, M. S., & Saikia, H. K. (2021). Irreducibility of A Formal Power Series with Integer Coefficients. The Journal of the Indian Mathematical Society, 88(3-4), 298–308. https://doi.org/10.18311/jims/2021/24897

Issue

Volume 88, Issue 3-4, July-December 2021

Section

Articles

License

Copyright (c) 2021 Mriganka S. Dutta, Helen K. Saikia

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Europe PMC
Received 2020-02-18
Accepted 2023-01-30
Published 2021-06-14

 

References

D. Birmajir, J. B. Gil, Arithmetic in the ring of formal power series with integer coeff icients, Amer. Math. Monthly, 115 (6), (2008), 541-549.

D. Birmajir, J. B. Gil and M. D. Weiner, Factoring polynomials in the ring of formal power series over Z, Int. J. Number Theory, 8 (7), (2012), 1763-1776.

D. Birmajir, J. B. Gil and M. D. Weiner, Factorization of quadratic polynomials in the ring of formal power series over Z, J. Algebra Appl., 6 (6), (2007), 1027-1037.

D. Birmajir, J. B. Gil and M. D. Weiner, On Hensel's roots and a factorization formula in Z[[x]], preprint, arXiv: 1308.2987 [math.NT], August 2013.

M. S. Dutta, Some classes of irreducible elements in formal power series ring over the set of integers, Int. J. Math. Archive, 4 (9), (2013), 278-282.

B. Fine and G. Rosenberger, The Fundamental Theorem of Algebra, Undergraduate Texts in Mathematics, Springer New York, 2012.

I. Kaplansky, Commutative Rings, Allyn and Bacon, Boston, MA, 1970.