Irreducibility criteria for factorial modules

Abstract

Let M be a torsion-free module over an integral domain R. The main results of this article provide analogue of Dumas irreducibility criterion and an extension of Eisenstein’s irreducibility criterion for factorial modules. Furthermore, we provide some applications of these results in $R[x]$-module $M[x]$.

keyword:

• Dumas criterion
• Eisenstein criterion
• factorial modules
• irreducibility

2020 Mathematics Subject Classification:

• 12E05
• 11R09

Acknowledgments

The authors are deeply grateful to the anonymous referee for carefully reading the paper and suggesting some changes which improved the paper.

Funding

Additional information

Funding

The first author is thankful to SERB grant SRG/2021/000393 and the second author is thankful to SERB grant SRG/2022/000236.