Quadratic forms over rings of dimension 1.
Quantum sections and Gauge algebras.
Using quantum sections of filtered rings and the associated Rees rings one can lift the scheme structure on Proj of the associated graded ring to the Proj of the Rees ring. The algebras of interest here are positively filtered rings having a non-commutative regular quadratic algebra for the associated graded ring; these are the so-called gauge algebras obtaining their name from special examples appearing in E. Witten's gauge theories. The paper surveys basic definitions and properties but concentrates...
Quasi-Excellence and Formal Series.
Quasi-Frobenius-Algebren und lokal vollständige Durchschnitte.
Quasiprime and d-prime ideals in commutative differential rings
Quintasymptotic primes, local cohomology and ideal topologies
Let Φ be a system of ideals on a commutative Noetherian ring R, and let S be a multiplicatively closed subset of R. The first result shows that the topologies defined by and are equivalent if and only if S is disjoint from the quintasymptotic primes of Φ. Also, by using the generalized Lichtenbaum-Hartshorne vanishing theorem we show that, if (R,) is a d-dimensional local quasi-unmixed ring, then , the dth local cohomology module of R with respect to Φ, vanishes if and only if there exists...
Quotient Rings of Polynomial Rings.
Regular Sequences in Rees and Symmetric Algebras I.
Remarks on Blowing-Up Divisorial Ideals.
Remarks on commutative noetherian rings whose flat modules have flat injective envelopes
Remarks on Noetherian local domains of dim 2.
Right Symbolic Powers and Classical Localization in Right Noetherian Rings.
Ringe mit nur endlich vielen Isomorphieklassen von maximalen, unzerlegbaren Cohen-Macaulay-Moduln.
-anneaux noethériens
Smooth algebras and vanishing of Hochschild homology.
Some Criteria for Rigidity of Noetherian Rings.
Some remarks on the altitude inequality
We introduce and study a new class of ring extensions based on a new formula involving the heights of their primes. We compare them with the classical altitude inequality and altitude formula, and we give another characterization of locally Jaffard domains, and domains satisfying absolutely the altitude inequality (resp., the altitude formula). Then we study the extensions R ⊆ S where R satisfies the corresponding condition with respect to S (Definition 3.1). This leads to a new characterization...
Some results on the cofiniteness of local cohomology modules
Let be a commutative Noetherian ring, an ideal of , an -module and a non-negative integer. In this paper we show that the class of minimax modules includes the class of modules. The main result is that if the -module is finite (finitely generated), is -cofinite for all and is minimax then is -cofinite. As a consequence we show that if and are finite -modules and is minimax for all then the set of associated prime ideals of the generalized local cohomology module...
Some results on top local cohomology modules with respect to a pair of ideals
Let and be ideals of a Noetherian local ring and let be a nonzero finitely generated -module. We study the relation between the vanishing of and the comparison of certain ideal topologies. Also, we characterize when the integral closure of an ideal relative to the Noetherian -module is equal to its integral closure relative to the Artinian -module .
Strict Mittag-Leffler conditions and locally split morphisms
In this paper, we prove that any pure submodule of a strict Mittag-Leffler module is a locally split submodule. As applications, we discuss some relations between locally split monomorphisms and locally split epimorphisms and give a partial answer to the open problem whether Gorenstein projective modules are Ding projective.