A realization of -groups
A reciprocity law for K2-traces.
A regularity criterion for semigroup rings.
A remark on a conjecture of Hain and Looijenga
We show that the natural generalization of a conjecture of Hain and Looijenga to the case of pointed curves holds for all and if and only if the tautological rings of the moduli spaces of curves with rational tails and of stable curves are Gorenstein.
A Remark on a Paper of Crachiola and Makar-Limanov
A. Crachiola and L. Makar-Limanov [J. Algebra 284 (2005)] showed the following: if X is an affine curve which is not isomorphic to the affine line , then ML(X×Y) = k[X]⊗ ML(Y) for every affine variety Y, where k is an algebraically closed field. In this note we give a simple geometric proof of a more general fact that this property holds for every affine variety X whose set of regular points is not k-uniruled.
A Remark on Almost Complete Intersections.
A remark on Hodge algebras and Gröbner bases
A remark on Koszul complexes.
A remark on projectively closed purities
A Remark on Pure Ideals and Projective Modules.
A Remark on Rings with Primary Ideals as Maximal Ideals.
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.