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### $\left(\delta ,2\right)$-primary ideals of a commutative ring

Czechoslovak Mathematical Journal

Let $R$ be a commutative ring with nonzero identity, let $ℐ\left(ℛ\right)$ be the set of all ideals of $R$ and $\delta :ℐ\left(ℛ\right)\to ℐ\left(ℛ\right)$ an expansion of ideals of $R$ defined by $I↦\delta \left(I\right)$. We introduce the concept of $\left(\delta ,2\right)$-primary ideals in commutative rings. A proper ideal $I$ of $R$ is called a $\left(\delta ,2\right)$-primary ideal if whenever $a,b\in R$ and $ab\in I$, then ${a}^{2}\in I$ or ${b}^{2}\in \delta \left(I\right)$. Our purpose is to extend the concept of $2$-ideals to $\left(\delta ,2\right)$-primary ideals of commutative rings. Then we investigate the basic properties of $\left(\delta ,2\right)$-primary ideals and also discuss the relations among $\left(\delta ,2\right)$-primary, $\delta$-primary and...

### A characterization of Krull rings with zero divisors

Archivum Mathematicum

It is proved that a Marot ring is a Krull ring if and only if its monoid of regular elements is a Krull monoid.

### A characterization of Prüfer rings.

Journal für die reine und angewandte Mathematik

### A class of multiplicative lattices

Czechoslovak Mathematical Journal

We study the multiplicative lattices $L$ which satisfy the condition $a=\left(a:\left(a:b\right)\right)\left(a:b\right)$ for all $a,b\in L$. Call them sharp lattices. We prove that every totally ordered sharp lattice is isomorphic to the ideal lattice of a valuation domain with value group $ℤ$ or $ℝ$. A sharp lattice $L$ localized at its maximal elements are totally ordered sharp lattices. The converse is true if $L$ has finite character.

### A class of torsion-free abelian groups characterized by the ranks of their socles

Czechoslovak Mathematical Journal

Butler groups formed by factoring a completely decomposable group by a rank one group have been studied extensively. We call such groups, bracket groups. We study bracket modules over integral domains. In particular, we are interested in when any bracket $R$-module is $R$ tensor a bracket group.

### A criterion for rings which are locally valuation rings

Colloquium Mathematicae

Using the notion of cyclically pure injective modules, a characterization of rings which are locally valuation rings is established. As applications, new characterizations of Prüfer domains and pure semisimple rings are provided. Namely, we show that a domain R is Prüfer if and only if two of the three classes of pure injective, cyclically pure injective and RD-injective modules are equal. Also, we prove that a commutative ring R is pure semisimple if and only if every R-module is cyclically pure...

### A General Theory of Almost Factoriality.

Manuscripta mathematica

### A local characterization of Prüfer rings.

Journal für die reine und angewandte Mathematik

### A note on the dual of a finitely generated multiplication module

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

### A strong complement property of Dedekind domains

Czechoslovak Mathematical Journal

### A structure theorem for sets of lengths

Colloquium Mathematicae

### A theory of multiplicity for multiplictive filtrations.

Journal für die reine und angewandte Mathematik

### A “$v$-operation free” approach to Prüfer $v$-multiplication domains.

International Journal of Mathematics and Mathematical Sciences

### A weakening of the euclidean property for integral domains and applications to algebraic number theory. II.

Journal für die reine und angewandte Mathematik

### A weakening of the euclidean property for integral domains and applications to algebraic number theory. I.

Journal für die reine und angewandte Mathematik

### Abelian Groups with an Endomorphism with Irreducible minimum Polynomial

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

### Almost Artinian modules.

Mathematica Scandinavica

### Almost Diagonal Matrices over Dedekind Domains.

Mathematische Zeitschrift

### Almost triangular matrices over Dedekind domains.

International Journal of Mathematics and Mathematical Sciences

### Arithmetic of block monoids

Mathematica Slovaca

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