A study of graded extremal rings and of monominal rings.
A subresultant theory of multivariate polynomials.
In Computer Algebra, Subresultant Theory provides a powerful method to construct algorithms solving problems for polynomials in one variable in an optimal way. So, using this method we can compute the greatest common divisor of two polynomials in one variable with integer coefficients avoiding the exponential growth of the coefficients that will appear if we use the Euclidean Algorithm.In this note, generalizing a forgotten construction appearing in [Hab], we extend the Subresultant Theory to the...
A subspace of and its connexions with the maximal ring of quotients
A Survey of Counterexamples to Hilbert's Fourteenth Problem
We survey counterexamples to Hilbert’s Fourteenth Problem, beginning with those of Nagata in the late 1950s, and including recent counterexamples in low dimension constructed with locally nilpotent derivations. Historical framework and pertinent references are provided. We also include 8 important open questions.
A survey on local cohomology and 𝓓-modules
A terminal area topology-independent GB-based conflict detection system for A-SMGCS.
A module for conflict detection in A-SMGCS is presented. It supervises the operations that the ground controller has to perform. It doesn?t depend on the topology of the terminal area. The system guarantees the safety of the proposed situation, that is, the impossibility that a conflict arises among aircrafts (and also road vehicles) obeying the signaling. We suppose that the terminal area has stop bars (or semaphores) controlling all intersections and accesses between runways, taxiways, exits,...
A Theorem of Grothendieck Using Picard Groups for the Algebraist.
A theorem on direct products of Slender modules
A theorem on normal flatness
A Theorem on Solutions of Analytic Equations with Applications to Deformations of Complex Structures.
A theory of multiplicity for multiplictive filtrations.
A two-dimensional domain whose integral closure is not t-linked.
A uniform Artin-Rees theorem and Zariski's main lemma on holomorphic functions.
A “-operation free” approach to Prüfer -multiplication domains.
A variant theory for the Gorenstein flat dimension
This paper discusses a variant theory for the Gorenstein flat dimension. Actually, since it is not yet known whether the category (R) of Gorenstein flat modules over a ring R is projectively resolving or not, it appears legitimate to seek alternate ways of measuring the Gorenstein flat dimension of modules which coincide with the usual one in the case where (R) is projectively resolving, on the one hand, and present nice behavior for an arbitrary ring R, on the other. In this paper, we introduce...
A weakening of the euclidean property for integral domains and applications to algebraic number theory. II.
A weakening of the euclidean property for integral domains and applications to algebraic number theory. I.
Abelian extensions of an absolutely unramified local field with general residue field.
Abelian group pairs having a trivial coGalois group
Torsion-free covers are considered for objects in the category Objects in the category are just maps in -Mod. For we find necessary and sufficient conditions for the coGalois group associated to a torsion-free cover, to be trivial for an object in Our results generalize those of E. Enochs and J. Rado for abelian groups.
Abelian groups which have trivial absolute coGalois group
In this article we characterize those abelian groups for which the coGalois group (associated to a torsion free cover) is equal to the identity.