A remark on the Hilbert series of tranversal polymatroids.
A remark on the quadratic analogue of the Quillen-Suslin theorem.
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