A remark on the spectra of rings with Gabriel dimension
A Remark on Two-Dimensional Local Rings with the Property of Approximation.
A remarkable contraction of semisimple Lie algebras
Recently, E.Feigin introduced a very interesting contraction of a semisimple Lie algebra (see arXiv:1007.0646 and arXiv:1101.1898). We prove that these non-reductive Lie algebras retain good invariant-theoretic properties of . For instance, the algebras of invariants of both adjoint and coadjoint representations of are free, and also the enveloping algebra of is a free module over its centre.
A restriction theorem and the Poincare series for U-invariants.
A set of generators for Ext...(k,k).
A Sharp Bound for the Minimal Number of Generators of Perfect Height Two Ideals.
A short note on the non-negativity of partial Euler characteristics.
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...