On the notions of characteristics and type for modules and their applications
On wsq-primary ideals
We introduce weakly strongly quasi-primary (briefly, wsq-primary) ideals in commutative rings. Let be a commutative ring with a nonzero identity and a proper ideal of . The proper ideal is said to be a weakly strongly quasi-primary ideal if whenever for some , then or Many examples and properties of wsq-primary ideals are given. Also, we characterize nonlocal Noetherian von Neumann regular rings, fields, nonlocal rings over which every proper ideal is wsq-primary, and zero dimensional...
Ore extensions over near pseudo-valuation rings.
Polynomial cycles in certain local domains
1. Let R be a domain and f ∈ R[X] a polynomial. A k-tuple of distinct elements of R is called a cycle of f if for i=0,1,...,k-2 and . The number k is called the length of the cycle. A tuple is a cycle in R if it is a cycle for some f ∈ R[X]. It has been shown in [1] that if R is the ring of all algebraic integers in a finite extension K of the rationals, then the possible lengths of cycles of R-polynomials are bounded by the number , depending only on the degree N of K. In this note we consider...
Polynomial Ring in Two Variables Over a D.V.R.: A Criterion.
Polyserial modules over valuation domains
P-orderings and polynomial functions on arbitrary subsets of Dedekind rings.
Proximity relations for real rank one valuations dominating a local regular ring.
We study 0-dimensional real rank one valuations centered in a regular local ring of dimension n > 2 such that the associated valuation ring can be obtained from the regular ring by a sequence of quadratic transforms. We define two classical invariants associated to the valuation (the refined proximity matrix and the multiplicity sequence) and we show that are equivalent data of the valuation.
Pseudo-valuation rings. II
Viene data una condizione sufficiente affinchè un sopra-anello di un anello di pseudo-valutazione (PVR) sia ancora un PVR. Da ciò segue che se è un PVR, allora ogni sopra-anello di è un PVR se (e soltanto se) è quasi-locale per ciascun elemento di . Vari risultati sono dimostrati per un ideale primo di un anello commutativo arbitrario , avente come insieme di zero-divisori. Per esempio, se è un primo «forte» di e contiene un elemento non-zero divisore di , allora è un sopra-anello...
Quasi-basic submodules over valuation domains
Quasi-seperable und koseperable Moduln über diskreten Bewertungsringen.
-поля
Rank-two torsion-free modules over valuation domains
Semigroups associated to singular points of plane curves.
Some cardinal invariants for valuation domains
Some properties of Butler modules over valuation domains
Sommes de puissances m-ièmes dans les anneaux β-adiques et les anneaux d'entiers algébriques
Spécialisation des revêtements en caractéristique
Stable Reduction and Uniformization of Abelian Varieties I.
Stable reduction and uniformization of abelian varieties II.