Topic
Algebraically compact module
About: Algebraically compact module is a research topic. Over the lifetime, 3 publications have been published within this topic receiving 50 citations.
Papers
1 Jan 1995
TL;DR: In this article, a finite-dimensional monomial algebraic module is constructed from a string module M(w) as a kind of completion, which is obtained from the corresponding string module m(w).
Abstract: Given a finite dimensional monomial algebra, one knows that some finite dimensional indecomposable modules may be described by words (finite sequences of letters) using as letters the arrows of the quiver and their formal inverses. To every word w, one can attach a so-called string module M(w). Here, we are going to construct certain infinite dimensional modules: We will consider ℕ-words and ℤ-words (thus infinite sequences of letters) satisfying suitable periodicity conditions. To every such ℕ-word or ℤ-word x, we describe an algebraically compact module C(x). This module C(x) is obtained from the corresponding string module M(x) as a kind of completion.
57 citations
1 Jun 2016
TL;DR: The notion of pure exact sequences was introduced in this article, where the authors define the notion of a pure exact sequence and establish several equivalent conditions for a pure sequence to be pure exact.
Abstract: In this paper, we introduce the notion of $$\chi $$
-pure exact sequence. An exact sequence $$0\longrightarrow A\longrightarrow B\longrightarrow C\longrightarrow 0$$
is said to be $$\chi $$
-pure-exact if $$0\longrightarrow A\bigotimes M\longrightarrow B\bigotimes M\longrightarrow C\bigotimes M\longrightarrow 0$$
is again an exact sequence, where A, B, C are right R-modules and $$M\simeq R/I$$
is a left R-module for $$I\in \chi $$
, where $$\chi $$
denotes the collection of left ideals of R. In this paper, we establish several equivalent conditions for a pure exact sequence to be $$\chi $$
-pure exact. We further define a $$\chi $$
-pure injective module and study the topological aspects of this module and introduce a condition under which a $$\chi $$
-pure injective module coincides with an algebraically compact module.
1 citations
TL;DR: In this article, it was shown that an artin algebra over an algebraically closed field all of whose algebraically compact (i.e., Σ-algebraically compact) indecomposable modules are finitely generated must be of finite representation type.
Abstract: The aim of this note is to prove that an artin algebra (resp. a finite dimensional algebra over an algebraically closed field) all of whose algebraically compact (resp. Σ-algebraically compact) indecomposable modules are finitely generated must be of finite-representation type. The result is derived with the aid of a theorem of Ziegler.
Performance Metrics
| Year | Papers |
|---|---|
| 2016 | 1 |
| 1995 | 1 |
| 1990 | 1 |