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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 .

Convex-compact sets and Banach discs

I. Monterde, Vicente Montesinos (2009)

Czechoslovak Mathematical Journal

Every relatively convex-compact convex subset of a locally convex space is contained in a Banach disc. Moreover, an upper bound for the class of sets which are contained in a Banach disc is presented. If the topological dual E ' of a locally convex space E is the σ ( E ' , E ) -closure of the union of countably many σ ( E ' , E ) -relatively countably compacts sets, then every weakly (relatively) convex-compact set is weakly (relatively) compact.

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