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### A characterization of subgroup lattices of finite abelian groups.

Beiträge zur Algebra und Geometrie

### A characterization of the Artinian modules.

Divulgaciones Matemáticas

### A Class of Balanced Non-Uniserial Rings.

Mathematische Annalen

### A criterion for quasi-heredity and the characteristic module.

Manuscripta mathematica

### A duality result for almost split sequences

Colloquium Mathematicae

Over an artinian hereditary ring R, we discuss how the existence of almost split sequences starting at the indecomposable non-injective preprojective right R-modules is related to the existence of almost split sequences ending at the indecomposable non-projective preinjective left R-modules. This answers a question raised by Simson in  in connection with pure semisimple rings.

### A Krull-Schmidt theorem for Artinian modules over local rings.

Zapiski Nauchnykh Seminarov POMI

### A note on hereditary rings or non-singular rings with chain condition.

Mathematica Scandinavica

### A representation theorem for Chain rings

Colloquium Mathematicae

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.

### Addendum to “Ring elements as sums of units”

Open Mathematics

We give a comment to Theorem 1.1 published in our paper “Ring elements as sums of units” [Cent. Eur. J. Math., 2009, 7(3), 395–399].

### An Application of a Theorem of Ziegler.

Monatshefte für Mathematik

### Anneaux semi-artiniens

Bulletin de la Société Mathématique de France

### Artinische Ringe mit artinischem Radikal.

Journal für die reine und angewandte Mathematik

### Characterizing rings by their modules

Banach Center Publications

### Closed extensions of R-modules in the case of a semi-artinian ring R

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si considerano le estensioni chiuse $B$ di un $R$-modulo $A$ mediante un $R$-modulo $C$ nel caso in cui $R$ sia un anello semi-artiniano, cioè un anello $R$ con la proprietà che per ogni quoziente $(R/_{I})\neq 0$ sia soc $(R/I)\neq 0$. Tali estensioni sono caratterizzate dal fatto che $A$ deve essere un sottomodulo semi-puro di $B$.

### Complexity and periodicity

Colloquium Mathematicae

Let M be a finitely generated module over an Artin algebra. By considering the lengths of the modules in the minimal projective resolution of M, we obtain the Betti sequence of M. This sequence must be bounded if M is eventually periodic, but the converse fails to hold in general. We give conditions under which it holds, using techniques from Hochschild cohomology. We also provide a result which under certain conditions guarantees the existence of periodic modules. Finally, we study the case when...

### Conditions which imply that subrings of artinian rings are artinian.

Journal für die reine und angewandte Mathematik

### C(X) vs. C(X) modulo its socle

Colloquium Mathematicae

Let ${C}_{F}\left(X\right)$ be the socle of C(X). It is shown that each prime ideal in $C\left(X\right)/{C}_{F}\left(X\right)$ is essential. For each h ∈ C(X), we prove that every prime ideal (resp. z-ideal) of C(X)/(h) is essential if and only if the set Z(h) of zeros of h contains no isolated points (resp. int Z(h) = ∅). It is proved that $dim\left(C\left(X\right)/{C}_{F}\left(X\right)\right)\ge dimC\left(X\right)$, where dim C(X) denotes the Goldie dimension of C(X), and the inequality may be strict. We also give an algebraic characterization of compact spaces with at most a countable number of nonisolated points. For each essential...

### Decomposition properties in modules categories

Acta Universitatis Carolinae. Mathematica et Physica

### Dually slender modules and steady rings.

Forum mathematicum

### Epis and monos which must be isos.

International Journal of Mathematics and Mathematical Sciences

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