A remark on power series rings.
A trivializability principle for local rings is described which leads to a form of weak algorithm for local semifirs with a finitely generated maximal ideal whose powers meet in zero.
A Remark on Projective Dimension of Fiat Modules.
A remark on projectively closed purities
A Remark on Pure Ideals and Projective Modules.
A Remark on Quadratic Spaces over Noncommutative Semilocal Rings.
A remark on quiver varieties and Weyl groups
In this paper we define an action of the Weyl group on the quiver varieties with generic .
A remark on regular right duo semigroups
A Remark on tilting theory and DG algebras.
A representation theorem for certain Boolean lattices.
Let R be an associative ring with 1 and R-tors the somplete Brouwerian lattice of all hereditary torsion theories on the category of left R-modules. A well known result asserts that R is a left semiartinian ring iff R-tors is a complete atomic Boolean lattice. In this note we prove that if L is a complete atomic Boolean lattice then there exists a left semiartinian ring R such that L is lattice-isomorphic to R-tors.
A representation theorem for Chain rings
A ring A is called a chain ring if it is a local, both sided artinian, principal ideal ring. Let R be a commutative chain ring. Let A be a faithful R-algebra which is a chain ring such that Ā = A/J(A) is a separable field extension of R̅ = R/J(R). It follows from a recent result by Alkhamees and Singh that A has a commutative R-subalgebra R₀ which is a chain ring such that A = R₀ + J(A) and R₀ ∩ J(A) = J(R₀) = J(R)R₀. The structure of A in terms of a skew polynomial ring over R₀ is determined.
A result of commutativity of rings.
A result on vanishing derivations for commutators on right ideals.
A Riemann-Roch theorem for dg algebras
Given a smooth proper dg algebra , a perfect dg -module and an endomorphism of , we define the Hochschild class of the pair with values in the Hochschild homology of the algebra . Our main result is a Riemann-Roch type formula involving the convolution of two such Hochschild classes.
A Riemann-Roch-Hirzebruch formula for traces of differential operators
Let be a holomorphic differential operator acting on sections of a holomorphic vector bundle on an -dimensional compact complex manifold. We prove a formula, conjectured by Feigin and Shoikhet, giving the Lefschetz number of as the integral over the manifold of a differential form. The class of this differential form is obtained via formal differential geometry from the canonical generator of the Hochschild cohomology of the algebra of differential operators on a formal neighbourhood of a...
A semigroup approach to wreath-product extensions of Solomon's descent algebras.
A short proof of Krull's intersection theorem
A short survey on Gorenstein global dimension
This text gives a short overview of the recent works on Gorenstein global dimension of rings.
A splitting theorem for multipeak path algebras
A splitting theorem for ℱ-products
A structure sheaf on the projective spectrum of a graded fully bounded Noetherian ring.