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Characterization of irreducible polynomials over a special principal ideal ring

Brahim Boudine (2023)

Mathematica Bohemica

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 .

Computing r -removed P -orderings and P -orderings of order h

Keith Johnson (2010)

Actes des rencontres du CIRM

We develop a recursive method for computing the r -removed P -orderings and P -orderings of order h , the characteristic sequences associated to these and limits associated to these sequences for subsets S of a Dedekind domain D . This method is applied to compute these objects for S = ℤ and S = ℤ ∖ p ℤ .

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