Split absolutely irreducible integer-valued polynomials over discrete valuation domains

On the factorization of polynomials over discrete valuation domains

We study some factorization properties for univariate polynomials with coefficients in a discrete valuation domain (A, v). We use some properties of the Newton index of a polynomial F (X) = ∑d i=0 aiX d−i ∈ A[X] to deduce conditions on v(ai) that allow us to find some information on the degree of the factors of F .

Integer-valued Polynomials over Quaternion Rings

When D is an integral domain with field of fractions K, the ring Int(D) = {f(x) ∈ K[x] | f(D) ⊆ D} of integer-valued polynomials over D has been extensively studied. We will extend the integer-valued polynomial construction to certain noncommutative rings. Specifically, let i, j, and k be the standard quaternion units satisfying the relations i = j = −1 and ij = k = −ji, and define ZQ := {a+bi+...

Filtered Modules over Discrete Valuation Domains

We consider a uni ed setting for studying local valuated groups and coset-valuated groups, emphasizing the associated ltrations rather than the values of elements. Stable exact sequences, projectives and injectives are identi ed in the encompassing category, and in the category corresponding to coset-valuated groups.

Generalizations of Dedekind domains and integer-valued polynomials

This talk will provide a snapshot of contemporary commutative algebra. In classical commutative algebra and algebraic number theory, the Dedekind domains are the most important class of rings. Modern commutative algebra studies numerous generalizations of the Dedekind domains in attempts to generalize results of algebraic number theory. This talk will introduce a few important generalizations o...

Irreducible Polynomials and Factorization Properties of the Ring of Integer-Valued Polynomials