A Counterexample to Artin Approximation With Respect to Subrings.
A criterion for detecting m-regularity.
A criterion for rings which are locally valuation rings
Using the notion of cyclically pure injective modules, a characterization of rings which are locally valuation rings is established. As applications, new characterizations of Prüfer domains and pure semisimple rings are provided. Namely, we show that a domain R is Prüfer if and only if two of the three classes of pure injective, cyclically pure injective and RD-injective modules are equal. Also, we prove that a commutative ring R is pure semisimple if and only if every R-module is cyclically pure...
A criterion for tangential flatness.
A database of invariant rings.
A differential criterion for complete intersections.
A Dimension Series for Multivariate Splines.
A directed -group that is not a group of divisibility
A factorization theorem for the polar of a curve with two branches
A Few Remarks on the Mohan Kumar Theorem
We give a simple geometric proof of Mohan Kumar's result about complete intersections.
A fibre criterion for a polynomial to belong to an ideal.
A finite ring polynomial.
A full uniform Artin-Rees theorem.
A functorial approach to the behaviour of multidimensional control systems
We show how to use the extension and torsion functors in order to compute the torsion submodule of a differential module associated with a multidimensional control system. In particular, we show that the concept of the weak primeness of matrices corresponds to the torsion-freeness of a certain module.
A -minimal model for principal -bundles
Sullivan associated a uniquely determined to any simply connected simplicial complex . This algebra (called minimal model) contains the total (and exactly) rational homotopy information of the space . In case is the total space of a principal -bundle, ( is a compact connected Lie-group) we associate a -equivariant model , which is a collection of “-homotopic” ’s with -action. will, in general, be different from the Sullivan’s minimal model of the space . contains the total rational...
A General Resolution for Grade Four Gorenstein Ideals.
A General Theory of Almost Factoriality.
A Generalization of Baer's Lemma
There is a classical result known as Baer’s Lemma that states that an -module is injective if it is injective for . This means that if a map from a submodule of , that is, from a left ideal of to can always be extended to , then a map to from a submodule of any -module can be extended to ; in other words, is injective. In this paper, we generalize this result to the category consisting of the representations of an infinite line quiver. This generalization of Baer’s Lemma...
A generalization of formal schemes and rigid analytic varieties.
A generalization of reflexive rings
We introduce a class of rings which is a generalization of reflexive rings and -reversible rings. Let be a ring with identity and denote the Jacobson radical of . A ring is called -reflexive if for any , implies . We give some characterizations of a -reflexive ring. We prove that some results of reflexive rings can be extended to -reflexive rings for this general setting. We conclude some relations between -reflexive rings and some related rings. We investigate some extensions of...