The Journal of the Indian Mathematical Society

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Irreducibility of A Formal Power Series with Integer Coefficients


Affiliations
1 Department of Mathematics, Nalbari College, Nalbari 781335, India
2 Department of Mathematics, Gauhati University, Guwahati 781014, India
     

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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
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  • Irreducibility of A Formal Power Series with Integer Coefficients

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Authors

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

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.

Keywords


Irreducible element, invertible element, factorization, formal power series ring

References





DOI: https://doi.org/10.18311/jims%2F2021%2F24897