A short proof of a fibre criterion for polynomials to belong to an ideal.
A short proof of Krull's intersection theorem
A simple characterization of principal ideal domains
1. Introduction. In this note we give necessary and sufficient conditions for an integral domain to be a principal ideal domain. Curiously, these conditions are similar to those that characterize Euclidean domains. In Section 2 we establish notation, discuss related results and prove our theorem. Finally, in Section 3 we give two nontrivial applications to real quadratic number fields.
A simple proof of uniqueness for torsion modules over principal ideal domains.
The aim of this note is to give an alternative proof of uniqueness for the decomposition of a finitely generated torsion module over a P.I.D. (= principal ideal domain) as a direct sum of indecomposable submodules.Our proof tries to mimic as far as we can the standard procedures used when dealing with vector spaces.For the sake of completeness we also include a proof of the existence theorem.
A simple solution of Hilbert's fourteenth problem in dimension five
We give a short proof of a counterexample (due to Daigle and Freudenburg) to Hilbert's fourteenth problem in dimension five.
A spectral construction of a treed domain that is not going-down
A splitting theorem for quadratic forms.
A standard basis approach to syzygies of canonical curves.
A strong complement property of Dedekind domains
A structure theorem for differential algebras
A structure theorem for sets of lengths
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