Normal and tangential flatness.
On prime modules over pullback rings
First, we give a complete description of the indecomposable prime modules over a Dedekind domain. Second, if is the pullback, in the sense of [9], of two local Dedekind domains then we classify indecomposable prime -modules and establish a connection between the prime modules and the pure-injective modules (also representable modules) over such rings.
On some classes of divisible modules
On some properties of polynomial rings.
On the dual of a finitely generated multiplication module II
On the ... in a Minimal Injective Resolution.
On the module of homomorphisms on finitely generated projective modules
On the product of a module by an ideal
On torsion Gorenstein injective modules
In this paper, we define Gorenstein injective rings, Gorenstein injective modules and their envelopes. The main topic of this paper is to show that if is a Gorenstein integral domain and is a left -module, then the torsion submodule of Gorenstein injective envelope of is also Gorenstein injective. We can also show that if is a torsion -module of a Gorenstein injective integral domain , then the Gorenstein injective envelope of is torsion.
Polynomial rings over Jacobson-Hilbert rings.
All rings considered are commutative with unit. A ring R is SISI (in Vámos' terminology) if every subdirectly irreducible factor ring R/I is self-injective. SISI rings include Noetherian rings, Morita rings and almost maximal valuation rings ([V1]). In [F3] we raised the question of whether a polynomial ring R[x] over a SISI ring R is again SISI. In this paper we show this is not the case.
Purity of the ideal of continuous functions with pseudocompact support.
Remarks on commutative noetherian rings whose flat modules have flat injective envelopes
-pure submodules.
Simple injective modules.
Some properties of the ideal of continuous functions with pseudocompact support.
Structure of flat covers of injective modules
The aim of this paper is to discuss the flat covers of injective modules over a Noetherian ring. Let R be a commutative Noetherian ring and let E be an injective R-module. We prove that the flat cover of E is isomorphic to . As a consequence, we give an answer to Xu’s question [10, 4.4.9]: for a prime ideal p, when does appear in the flat cover of E(R/m̲)?
Sur la compacité du spectre minimal d'un anneau
Sur les modules linéairement compacts
The dual notion of prime submodules
In this paper the concept of the second submodule (the dual notion of prime submodule) is introduced.
The first term in a minimal pure injective resolution.