EuDML | Browse

The study of stable equivalences of finite-dimensional algebras over an algebraically closed field seems to be far from satisfactory results. The importance of problems concerning stable equivalences grew up when derived categories appeared in representation theory of finite-dimensional algebras [8]. The Tachikawa-Wakamatsu result [17] also reveals the importance of these problems in the study of tilting equivalent algebras (compare with [1]). In fact, the result says that if A and B are tilting...

Algebras whose Euler form is non-negative

M. Barot, J. de la Peña (1999)

Colloquium Mathematicae

Algebren, Darstellungsköcher, Ueberlagerungen und zurück.

C. Riedtmann (1980)

Commentarii mathematici Helvetici

Algèbres auto-injectives de représentation finie

Pierre Gabriel (1979/1980)

Séminaire Bourbaki

Algèbres de Bass et extensions de Ore itérées.

Marie-Paule Malliavin (1994)

Collectanea Mathematica

We show that some iterated Ore extensions have the same behaviour with respect to injective resolutions as Gorenstein commutative rings.

Algèbres de type de représentation fini

Christine Riedtmann (1984/1985)

Séminaire Bourbaki

Almost Abelian rings

Junchao Wei (2013)

Communications in Mathematics

A ring $R$ is defined to be left almost Abelian if $a e = 0$ implies $a R e = 0$ for $a \in N (R)$ and $e \in E (R)$ , where $E (R)$ and $N (R)$ stand respectively for the set of idempotents and the set of nilpotents of $R$ . Some characterizations and properties of such rings are included. It follows that if $R$ is a left almost Abelian ring, then $R$ is $π$ -regular if and only if $N (R)$ is an ideal of $R$ and $R / N (R)$ is regular. Moreover it is proved that (1) $R$ is an Abelian ring if and only if $R$ is a left almost Abelian left idempotent reflexive ring. (2) $R$ is strongly...

Almost smooth algebras

Alfredo R. Grandjean, Maria J. Vale (1991)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Almost split sequences and module categories: A complementary view to Auslander-Reiten Theory

Ariel Fernández (1995)

Commentationes Mathematicae Universitatis Carolinae

We take a complementary view to the Auslander-Reiten trend of thought: Instead of specializing a module category to the level where the existence of an almost split sequence is inferred, we explore the structural consequences that result if we assume the existence of a single almost split sequence under the most general conditions. We characterize the structure of the bimodule $_{Δ} E x t_{R} {(C, A)}_{Γ}$ with an underlying ring $R$ solely assuming that there exists an almost split sequence of left $R$ -modules $0 \to A \to B \to C \to 0$ . $Δ$ and $Γ$ are...

Almost split sequences for non-regular modules

S. Liu (1993)

Fundamenta Mathematicae

Let A be an Artin algebra and let $0 \to X \to \oplus_{i = 1}^{r} Y_{i} \to Z \to 0$ be an almost split sequence of A-modules with the $Y_{i}$ indecomposable. Suppose that X has a projective predecessor and Z has an injective successor in the Auslander-Reiten quiver $Γ_{A}$ of A. Then r ≤ 4, and r = 4 implies that one of the $Y_{i}$ is projective-injective. Moreover, if $X \to \oplus_{j = 1}^{t} Y_{j}$ is a source map with the $Y_{j}$ indecomposable and X on an oriented cycle in $Γ_{A}$ , then t ≤ 4 and at most three of the $Y_{j}$ are not projective. The dual statement for a sink map holds. Finally, if an arrow...

Almost Split Sequences over p-adic Rings.

J.A. Green, M.T.A.D. Nogueira (1988)

Mathematische Zeitschrift

Almost-flat modules

Simion Breaz (2003)

Czechoslovak Mathematical Journal

We present general properties for almost-flat modules and we prove that a self-small right module is almost flat as a left module over its endomorphism ring if and only if the class of $g$ -static modules is closed under the kernels.

The aim of this note is to express a module which is localized as well as colocalized in terms of an object of an intersecting subcategory related to static modules.

Currently displaying 81 – 100 of 122

Previous Page 5 Next

Displaying 81 – 100 of 122

Additive Duality at Cosmall Injectives

Adjoints, torsion theory and purity.

AGQP-injective modules.

Algebraically compact modules

Algebraically Compact Rings and Modules.

Algebras stably equivalent to trivial extensions of hereditary algebras of type $Ã_{n}$