Open Access
Subscription Access
Open Access
Subscription Access
Irreducibility of A Formal Power Series with Integer Coefficients
Subscribe/Renew Journal
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.
Keywords
Irreducible element, invertible element, factorization, formal power series ring
Subscription
Login to verify subscription
User
Font Size
Information
- 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 ischolar_mains 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.
Abstract Views: 475
PDF Views: 0