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Irreducibility of a sum of polynomials depending on disjoint sets of variables

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Abstract

In this article, we give two different sufficient conditions for the irreducibility of a polynomial of more than one variable, over an algebraically closed field, that can be written as a sum of two polynomials which depend on mutually disjoint sets of variables. These conditions are derived from analyzing the Newton polytope of such a polynomial and then applying the ‘Irreducibility criterion’ introduced by Gao.

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Acknowledgements

A part of this work was carried out at the Indian Institute of Science (IISc), Bangalore where the first author was a research associate. He wishes to thank his thesis adviser Professor Gautam Bharali for supporting him at this position under his Swarnajayanti Fellowship (Grant No. DST/SJF/MSA-02/2013-14). Vikramjeet Singh Chandel was supported by an Institute Postdoctoral Fellowship of IIT Bombay while working on this project.

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Correspondence to Vikramjeet Singh Chandel.

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Communicated by Gurmeet Kaur Bakshi.

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Chandel, V.S., Dayal, U. Irreducibility of a sum of polynomials depending on disjoint sets of variables. Indian J Pure Appl Math 53, 609–616 (2022). https://doi.org/10.1007/s13226-021-00152-2

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  • DOI: https://doi.org/10.1007/s13226-021-00152-2

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