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Characterization of irreducible polynomials over a special principal ideal ring

. 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 .