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A NOTE ON GIRSTMAIR’S IRREDUCIBILITY CRITERION

Part of: Polynomials and matrices General field theory

Published online by Cambridge University Press:  04 November 2021

JITENDER SINGH Open the ORCID record for JITENDER SINGH [Opens in a new window]  and
SANJEEV KUMAR Open the ORCID record for SANJEEV KUMAR [Opens in a new window]
JITENDER SINGH
Affiliation:
Department of Mathematics, Guru Nanak Dev University, Amritsar 143005, India e-mail: sonumaths@gmail.com
SANJEEV KUMAR*
Affiliation:
Department of Mathematics, SGGS College, Sector 26, Chandigarh 160019, India
*
e-mail: sanjeev_kumar_19@yahoo.co.in
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Abstract

Girstmair [‘On an irreducibility criterion of M. Ram Murty’, Amer. Math. Monthly 112(3) (2005), 269–270] gave a generalisation of Ram Murty’s irreducibility criterion. We further generalise these criteria.

Keywords

irreducible polynomialirreducibility criterion

MSC classification

Primary: 12E05: Polynomials (irreducibility, etc.)
Secondary: 11C08: Polynomials
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 106 , Issue 1 , August 2022 , pp. 62 - 66
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

This research is supported by the Science and Engineering Research Board (SERB), a statutory body of the Department of Science and Technology (DST), Government of India, through the project grant no. MTR/2017/000575 awarded to the first author under the MATRICS scheme.

References

Girstmair, K., ‘On an irreducibility criterion of M. Ram Murty’, Amer. Math. Monthly 112(3) (2005), 269–270.CrossRefGoogle Scholar
Ram Murty, M., ‘Prime numbers and irreducible polynomials’, Amer. Math. Monthly 109(5) (2002), 452–458.Google Scholar
Singh, J. and Kumar, S., ‘A new class of irreducible polynomials’, Comm. Algebra 49(6) (2021), 2722–2727.Google Scholar