A Cancellation Theorem for Artinian Local Algebras.
A characterization of commutative Fréchet algebras with all ideals closed
Let A be a commutative unital Fréchet algebra, i.e. a completely metrizable topological algebra. Our main result states that all ideals in A are closed if and only if A is a noetherian algebra
A characterization of F-algebras with all one-sided ideals closed
We prove that a real or complex F-algebra has all left and right ideals closed if and only if it is noetherian.
A criterion for tangential flatness.
A generalization of the Auslander transpose and the generalized Gorenstein dimension
Let be a left and right Noetherian ring and a semidualizing -bimodule. We introduce a transpose of an -module with respect to which unifies the Auslander transpose and Huang’s transpose, see Z. Y. Huang, On a generalization of the Auslander-Bridger transpose, Comm. Algebra 27 (1999), 5791–5812, in the two-sided Noetherian setting, and use to develop further the generalized Gorenstein dimension with respect to . Especially, we generalize the Auslander-Bridger formula to the generalized...
A Note On A Class Of Noetherian Rings
A note on a class of Noetherian rings.
A note on local Noether lattices
A note on the countable union of prime submodules.
À propos d'un théorème de Mori-Nagata
A short note on the non-negativity of partial Euler characteristics.
A study of graded extremal rings and of monominal rings.
A theory of multiplicity for multiplictive filtrations.
About Nagata Rings.
Addendum zu: Quasi-Frobenius-Algebren und lokal vollständige Durchschnitte:
Algebraische Eigenschaften der lokalen Ringe in den Spitzen der Hilbertschen Modulgruppen.
An Application of Jonsson Modules to Some Questions Concerning Proper Subrings.
Anneaux de Goldman
Anneaux excellents en caractéristique zéro
Annihilators of local homology modules
Let be a local ring, an ideal of and a nonzero Artinian -module of Noetherian dimension with . We determine the annihilator of the top local homology module . In fact, we prove that where denotes the smallest submodule of such that . As a consequence, it follows that for a complete local ring all associated primes of are minimal.