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 corollary to the Evans-Griffith Syzygy theorem
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 generalization of the finiteness problem of the local cohomology modules
Let be a commutative Noetherian ring and an ideal of . We introduce the concept of -weakly Laskerian -modules, and we show that if is an -weakly Laskerian -module and is a non-negative integer such that is -weakly Laskerian for all and all , then for any -weakly Laskerian submodule of , the -module is -weakly Laskerian. In particular, the set of associated primes of is finite. As a consequence, it follows that if is a finitely generated -module and is an -weakly...
A Note On A Class Of Noetherian Rings
A note on a class of Noetherian rings.
A note on indecomposable projective modules
A note on local Noether lattices
A note on the countable union of prime submodules.
A Product Theorem for Lattices over Orders.
À propos d'un théorème de Mori-Nagata
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.
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: