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On prolongations of rank one discrete valuations

Lhoussain El Fadil (2019)

Commentationes Mathematicae Universitatis Carolinae

Let ( K , ν ) be a valued field, where ν is a rank one discrete valuation. Let R be its ring of valuation, 𝔪 its maximal ideal, and L an extension of K , defined by a monic irreducible polynomial F ( X ) ∈ R [ X ] . Assume that F ¯ ( X ) factors as a product of r distinct powers of monic irreducible polynomials. In this paper a condition which guarantees the existence of exactly r distinct valuations of K extending ν is given, in such a way that it generalizes the results given in the paper “Prolongations of valuations to finite...

On proximity relations for valuations dominating a two-dimensional regular local ring.

José J. Aparicio, Angel Granja, Tomás Sánchez-Giralda (1999)

Revista Matemática Iberoamericana

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 pseudo-prime multiplication modules over pullback rings

Fatemeh Esmaeili Khalil Saraei (2016)

Colloquium Mathematicae

The purpose of this paper is to present a new approach to the classification of indecomposable pseudo-prime multiplication modules over pullback of two local Dedekind domains. We extend the definitions and the results given by Ebrahimi Atani and Farzalipour (2009) to more general cases.

On quasi n -ideals of commutative rings

Adam Anebri, Najib Mahdou, Emel Aslankarayiğit Uğurlu (2022)

Czechoslovak Mathematical Journal

Let R be a commutative ring with a nonzero identity. In this study, we present a new class of ideals lying properly between the class of n -ideals and the class of ( 2 , n ) -ideals. A proper ideal I of R is said to be a quasi n -ideal if I is an n -ideal of R . Many examples and results are given to disclose the relations between this new concept and others that already exist, namely, the n -ideals, the quasi primary ideals, the ( 2 , n ) -ideals and the p r -ideals. Moreover, we use the quasi n -ideals to characterize some...

On reconstructing algebraic sets and ideals

Paweł Gniadek (2007)

Annales Polonici Mathematici

We generalize some results on reconstructing sets to the case of ideals of 𝕜[X₁,...,Xₙ]. We show that reconstructing sets can be approximated by finite subsets having the property of reconstructing automorphisms of bounded degree.

On reconstruction of polynomial automorphisms

Paweł Gniadek (1996)

Annales Polonici Mathematici

We extend results on reconstructing a polynomial automorphism from its restriction to the coordinate hyperplanes to some wider class of algebraic surfaces. We show that the algorithm proposed by M. Kwieciński in [K2] and based on Gröbner bases works also for this class of surfaces.

On rings of constants of derivations in two variables in positive characteristic

Piotr Jędrzejewicz (2006)

Colloquium Mathematicae

Let k be a field of chracteristic p > 0. We describe all derivations of the polynomial algebra k[x,y], homogeneous with respect to a given weight vector, in particular all monomial derivations, with the ring of constants of the form k [ x p , y p , f ] , where f ∈ k [ x , y ] ∖ k [ x p , y p ] .

Currently displaying 141 – 160 of 389