On polynomials whose fibres are irreducible with no critical points.
On prime divisors of the integral closure of a principal ideal.
On prime modules over pullback rings
First, we give a complete description of the indecomposable prime modules over a Dedekind domain. Second, if is the pullback, in the sense of [9], of two local Dedekind domains then we classify indecomposable prime -modules and establish a connection between the prime modules and the pure-injective modules (also representable modules) over such rings.
On prime submodules and primary decomposition
We characterize prime submodules of for a principal ideal domain and investigate the primary decomposition of any submodule into primary submodules of
On proximity relations for valuations dominating a two-dimensional regular local ring.
The purpose of this paper is to define a new numerical invariant of valuations centered in a regular two-dimensional regular local ring. For this, we define a sequence of non-negative rational numbers δν = {δν(j)}j ≥ 0 which is determined by the proximity relations of the successive quadratic transformations at the points determined by a valuation ν. This sequence is characterized by seven combinatorial properties, so that any sequence of non-negative rational numbers having the above properties...
On Prüfer domains of polynomials.
On Prüfer v-Multiplication Domains.
On Quasi Divisor Theories and Systems of Valuations.
On quasi-projective uniserial modules
On radical-equivalent and zero-equivalent ideals
On roots of polynomials with power series coefficients
We give a deepened version of a lemma of Gabrielov and then use it to prove the following fact: if h ∈ 𝕂[[X]] (𝕂 = ℝ or ℂ) is a root of a non-zero polynomial with convergent power series coefficients, then h is convergent.
On semicontinuity of ramification invariants in dimension 2.
On some classes of divisible modules
On some generalizations of Jacobi's residue formula
On some issues concerning polynomial cycles
We consider two issues concerning polynomial cycles. Namely, for a discrete valuation domain of positive characteristic (for ) or for any Dedekind domain of positive characteristic (but only for ), we give a closed formula for a set of all possible cycle-lengths for polynomial mappings in . Then we give a new property of sets , which refutes a kind of conjecture posed by W. Narkiewicz.
On some noetherian rings of germs on a real closed field
Let R be a real closed field, and denote by the ring of germs, at the origin of Rⁿ, of functions in a neighborhood of 0 ∈ Rⁿ. For each n ∈ ℕ, we construct a quasianalytic subring with some natural properties. We prove that, for each n ∈ ℕ, is a noetherian ring and if R = ℝ (the field of real numbers), then , where ₙ is the ring of germs, at the origin of ℝⁿ, of real analytic functions. Finally, we prove the Real Nullstellensatz and solve Hilbert’s 17th Problem for the ring .
On some partial orders associated to generic initial ideals.
On some properties of polynomial rings.
On standard basis and multiplicity of .
On Stanley-Reisner rings