On a generalization of a Prüfer-Kaplansky-Procházka theorem
On chains of centered valuations.
On chains of free modules over valuation domains
On -rings that are not formally real
Henriksen and Isbell showed in 1962 that some commutative rings admit total orderings that violate equational laws (in the language of lattice-ordered rings) that are satisfied by all totally-ordered fields. In this paper, we review the work of Henriksen and Isbell on this topic, construct and classify some examples that illustrate this phenomenon using the valuation theory of Hion (in the process, answering a question posed in [E]) and, finally, prove that a base for the equational theory of totally-ordered...
On *-modules over valuation rings
On -ideals of groups of divisibility
On prolongations of rank one discrete valuations
Let be a valued field, where is a rank one discrete valuation. Let be its ring of valuation, its maximal ideal, and an extension of , defined by a monic irreducible polynomial . Assume that factors as a product of distinct powers of monic irreducible polynomials. In this paper a condition which guarantees the existence of exactly distinct valuations of extending is given, in such a way that it generalizes the results given in the paper “Prolongations of valuations to finite...
On Prüfer v-Multiplication Domains.
On Quasi Divisor Theories and Systems of Valuations.
On quasi -ideals of commutative rings
Let be a commutative ring with a nonzero identity. In this study, we present a new class of ideals lying properly between the class of -ideals and the class of -ideals. A proper ideal of is said to be a quasi -ideal if is an -ideal of Many examples and results are given to disclose the relations between this new concept and others that already exist, namely, the -ideals, the quasi primary ideals, the -ideals and the -ideals. Moreover, we use the quasi -ideals to characterize some...
On relative real holomorphy rings.
On ruled fields
Some results and problems that arise in connection with the foundations of the theory of ruled and rational field extensions are discussed.
On the closed subfields of [...] Q ¯ p
Let p be a prime number, and let [...] Q¯ p be the completion of Q with respect to the pseudovaluation w which extends the p-adic valuation vp. In this paper our goal is to give a characterization of closed subfields of [...] Q¯ p , the completion of Q with respect w, i.e. the spectral extension of the p-adic valuation vp on Q.
On the Graded Algebra relative to a valuation.
On the Jung method in positive characteristic
Let be a germ of normal surface with local ring covering a germ of regular surface with local ring of characteristic . Given an extension of valuation rings birationally dominating , we study the existence of a new such pair of local rings birationally dominating , such that is regular and has only toric singularities. This is achieved when is defectless or when is equal to
On the local uniformization problem
In this paper we give a short introduction to the local uniformization problem. This follows a similar line as the one presented by the second author in his talk at ALANT 3. We also discuss our paper on the reduction of local uniformization to the rank one case. In that paper, we prove that in order to obtain local uniformization for valuations centered at objects of a subcategory of the category of noetherian integral domains, it is enough to prove it for rank one valuations centered at objects...
On the Poincaré series for a plane divisorial valuation.
On the Prime Ideal of an Ordering of Higher Level.
On the Weierstrass division.
On valuation spectra