A module is called uniserial if it has totally ordered submodules in inclusion. We describe direct summands of for a uniserial module . It appears that any such a summand is isomorphic to a direct sum of copies of at most two uniserial modules.
Addendum to the author's article "Rings whose modules have maximal submodules", which appeared in Publicacions Matemàtiques 39, 1 (1995), 201-214.
We list some typos and minor correction that in no way affect the main results of Rings with zero intersection property on annihilators: Zip rings (Publicacions Matemàtiques 33, 2 (1989), pp. 329-338), e.g., nothing stated in the abstract is affected.
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...
We show that some iterated Ore extensions have the same behaviour with respect to injective resolutions as Gorenstein commutative rings.
A ring is defined to be left almost Abelian if implies for and , where and stand respectively for the set of idempotents and the set of nilpotents of . Some characterizations and properties of such rings are included. It follows that if is a left almost Abelian ring, then is -regular if and only if is an ideal of and is regular. Moreover it is proved that (1) is an Abelian ring if and only if is a left almost Abelian left idempotent reflexive ring. (2) is strongly...
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 with an underlying ring solely assuming that there exists an almost split sequence of left -modules . and are...
Let A be an Artin algebra and let be an almost split sequence of A-modules with the indecomposable. Suppose that X has a projective predecessor and Z has an injective successor in the Auslander-Reiten quiver of A. Then r ≤ 4, and r = 4 implies that one of the is projective-injective. Moreover, if is a source map with the indecomposable and X on an oriented cycle in , then t ≤ 4 and at most three of the are not projective. The dual statement for a sink map holds. Finally, if an arrow...
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 -static modules is closed under the kernels.