Mathematica Bohemica

Mathematica Bohemica, Vol. 148, No. 4, pp. 501-506, 2023

Characterization of irreducible polynomials over a special principal ideal ring

Brahim Boudine

Received December 5, 2021. Published online September 8, 2022.

Abstract: A commutative ring $R$ with unity is called a special principal ideal ring (SPIR) if it is a non integral principal ideal ring containing only one nonzero prime ideal, its length $e$ is the index of nilpotency of its maximal ideal. In this paper, we show a characterization of irreducible polynomials over a SPIR of length $2$. Then, we give a sufficient condition for a polynomial to be irreducible over a SPIR of any length $e$.

Keywords: polynomial; irreducibility; commutative principal ideal ring

Classification MSC: 13F20, 13B25

DOI: 10.21136/MB.2022.0187-21

PDF available at: Institute of Mathematics CAS

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Affiliations: Brahim Boudine, Faculty of Sciences Dhar El Mahraz, University Sidi Mohamed Ben Abdellah, Fez, Morocco, e-mail: brahimboudine.bb@gmail.com

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