La condition « intégralement clos », IV, modules de type fini sur un ordre maximal
La dimension de Gel'fand-Kirillov
La filtrazione di Gabriel - II
Le foncteur entre -espaces vectoriels est noethérien
Les foncteurs entre espaces vectoriels, ou représentations génériques des groupes linéaires d’après Kuhn, interviennent en topologie algébrique et en -théorie comme en théorie des représentations. Nous présentons ici une nouvelle méthode pour aborder les problèmes de finitude et la dimension de Krull dans ce contexte.Plus précisément, nous démontrons que, dans la catégorie des foncteurs entre espaces vectoriels sur , le produit tensoriel entre , où désigne le foncteur projectif , et un foncteur...
Left APP-property of formal power series rings
A ring is called a left APP-ring if the left annihilator is right -unital as an ideal of for any element . We consider left APP-property of the skew formal power series ring where is a ring automorphism of . It is shown that if is a ring satisfying descending chain condition on right annihilators then is left APP if and only if for any sequence of elements of the ideal
Left EM rings
Let be the polynomial ring over a ring with unity. A polynomial is referred to as a left annihilating content polynomial (left ACP) if there exist an element and a polynomial such that and is not a right zero-divisor polynomial in . A ring is referred to as left EM if each polynomial is a left ACP. We observe the structure of left EM rings with various properties, and study the relationships between the one-sided EM condition and other standard ring theoretic conditions. Moreover,...
Lengths of Submodule Chains Versus Krull Dimension in Non-Noetherian Modules.
Linearly Compact Rings and Modules.
Local cohomology in classical rings.
The aim of this paper is to establish the close connection between prime ideals and torsion theories in a non necessarily commutative noetherian ring. We introduce a new definition of support of a module and characterize some kinds of torsion theories in terms of prime ideals. Using the machinery introduced before, we prove a version of the Mayer-Vietoris Theorem for local cohomology and establish a relationship between the classical dimension and the vanishing of the groups of local cohomology...
Local rings of order with 4-nilpotent Jacobson radical.
Localisation à la manière de Goldie et applications
Localisations et anneaux semi-noethériens à droite
Localisations premières
Localization and Artinian Quotient Rings.
Localization in Prime Noetherian p.i. Rings.
Localizations of Hereditary Noetherian Rings
Loewy coincident algebra and -3 associated graded algebra
We prove that an associated graded algebra of a finite dimensional algebra is (= selfinjective) if and only if is and Loewy coincident. Here is said to be Loewy coincident if, for every primitive idempotent , the upper Loewy series and the lower Loewy series of and coincide. -3 algebras are an important generalization of algebras; note that Auslander algebras form a special class of these algebras. We prove that for a Loewy coincident algebra , the associated graded algebra...
Lokalinvariante Bewertungen.
Lower Bounds for faithful, preinjective modules.
L-zero-divisor graphs of direct products of L-commutative rings
L-zero-divisor graphs of L-commutative rings have been introduced and studied in [5]. Here we consider L-zero-divisor graphs of a finite direct product of L-commutative rings. Specifically, we look at the preservation, or lack thereof, of the diameter and girth of the L-ziro-divisor graph of a L-ring when extending to a finite direct product of L-commutative rings.