A Class of Balanced Non-Uniserial Rings.
A general form of non-Frobenius self-injective algebras
Applying the classical work of Nakayama [Ann. of Math. 40 (1939)], we exhibit a general form of non-Frobenius self-injective finite-dimensional algebras over a field.
A Krull-Schmidt theorem for Artinian modules over local rings.
A noncommutative generalization of Auslander's last theorem.
A note on -cofinitely supplemented modules.
A note on functors that vanish on indecomposable modules.
A note on perfect rings.
A note on semilocal group rings
Let be an associative ring with identity and let denote the Jacobson radical of . is said to be semilocal if is Artinian. In this paper we give necessary and sufficient conditions for the group ring , where is an abelian group, to be semilocal.
A remark on power series rings.
A trivializability principle for local rings is described which leads to a form of weak algorithm for local semifirs with a finitely generated maximal ideal whose powers meet in zero.
A Remark on Quadratic Spaces over Noncommutative Semilocal Rings.
A representation theorem for Chain rings
A ring A is called a chain ring if it is a local, both sided artinian, principal ideal ring. Let R be a commutative chain ring. Let A be a faithful R-algebra which is a chain ring such that Ā = A/J(A) is a separable field extension of R̅ = R/J(R). It follows from a recent result by Alkhamees and Singh that A has a commutative R-subalgebra R₀ which is a chain ring such that A = R₀ + J(A) and R₀ ∩ J(A) = J(R₀) = J(R)R₀. The structure of A in terms of a skew polynomial ring over R₀ is determined.
A structure theorem for right invariant right holoids.
A subclass of strongly clean rings
In this paper, we introduce a subclass of strongly clean rings. Let be a ring with identity, be the Jacobson radical of , and let denote the set of all elements of which are nilpotent in . An element is called very -clean provided that there exists an idempotent such that and or is an element of . A ring is said to be very -clean in case every element in is very -clean. We prove that every very -clean ring is strongly -rad clean and has stable range one. It is shown...
Addendum to "Rings whose modules have maximal submodules".
Addendum to the author's article "Rings whose modules have maximal submodules", which appeared in Publicacions Matemàtiques 39, 1 (1995), 201-214.
Addendum to Zip rings.
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.
Addendum zu: Quasi-Frobenius-Algebren und lokal vollständige Durchschnitte:
Algebras stably equivalent to trivial extensions of hereditary algebras of type
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...
Algebren, Darstellungsköcher, Ueberlagerungen und zurück.
Almost approximately convex functions
An action-free characterization of weak Hopf-Galois extensions.