Die absteigende Loewy-Länge von Endomorphismenringen.
Die Struktur von projektiven Moduln.
Differentially trivial Noetherian semiperfect rings.
Épimorphismes plats à buts locaux, quasi-locaux et semi-locaux
Erratum to "On rings with a unique proper essential right ideal" (Fund. Math. 183 (2004), 229-244)
Exchange Rings and Decompositions of Modules.
Fastgeordnete und geordnete lokale Ringe und ihre geometrische Anwendung
F-semiperfeke und perfekte Moduln in ... [M].
Green walks in a hypergraph
Noncommutative Valuation Rings
Non-perfect rings and a theorem of Eklof and Shelah
We prove a stronger form, , of a consistency result, , due to Eklof and Shelah. concerns extension properties of modules over non-left perfect rings. We also show (in ZFC) that does not hold for left perfect rings.
On certain classes of modules.
Let X be a class or R-modules containing 0 and closed under isomorphic images. With any such X we associate three classes ΓX, FX and ΔX. The study of some of the closure properties of these classes allows us to obtain characterization of Artinian modules dualizing results of Chatters. The theory of Dual Glodie dimension as developed by the author in some of his earlier work plays a crucial role in the present paper.
On local QF rings.
On rings with a unique proper essential right ideal
Right ue-rings (rings with the property of the title, i.e., with the maximality of the right socle) are investigated. It is shown that a semiprime ring R is a right ue-ring if and only if R is a regular V-ring with the socle being a maximal right ideal, and if and only if the intrinsic topology of R is non-discrete Hausdorff and dense proper right ideals are semisimple. It is proved that if R is a right self-injective right ue-ring (local right ue-ring), then R is never semiprime and is Artin semisimple...
On subgroups of GL2 over non-commutative local rings which are normalized by elementary matrices.
On the existence of projective and quasi-projective covers
On Two-Sided Right Ideals in Chain Domains.
Ore sets in enveloping algebras
Perfect rings for which the converse of Schur's lemma holds.
If M is a simple module over a ring R then, by the Schur's lemma, the endomorphism ring of M is a division ring. However, the converse of this result does not hold in general, even when R is artinian. In this short note, we consider perfect rings for which the converse assertion is true, and we show that these rings are exactly the primary decomposable ones.
Prime PI-rights in which finitely generated right ideals are principal.