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### A General Theory of Almost Factoriality.

Manuscripta mathematica

### A note on projective modules and multiplication modules

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

### A simple characterization of principal ideal domains

Acta Arithmetica

1. Introduction. In this note we give necessary and sufficient conditions for an integral domain to be a principal ideal domain. Curiously, these conditions are similar to those that characterize Euclidean domains. In Section 2 we establish notation, discuss related results and prove our theorem. Finally, in Section 3 we give two nontrivial applications to real quadratic number fields.

### 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

### An addendum to the paper: “Arithmetic functions over rings with zero divisors” by Ruangsinsap, Laohakosol and P. Udomkavanich.

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

### Arithmetic functions over rings with zero divisors.

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

### Arithmetic of non-principal orders in algebraic number fields

Actes des rencontres du CIRM

Let $R$ be an order in an algebraic number field. If $R$ is a principal order, then many explicit results on its arithmetic are available. Among others, $R$ is half-factorial if and only if the class group of $R$ has at most two elements. Much less is known for non-principal orders. Using a new semigroup theoretical approach, we study half-factoriality and further arithmetical properties for non-principal orders in algebraic number fields.

Acta Arithmetica

### Atomicity and the fixed divisor in certain pullback constructions

Colloquium Mathematicae

Let D be an integral domain with field of fractions K. In this article, we use a certain pullback construction in the spirit of Int(E,D) that furnishes many examples of domains between D[x] and K[x] in which there are elements that do not admit a finite factorization into irreducible elements. We also define the notion of a fixed divisor for this pullback construction to characterize all of its irreducible elements and those nonzero nonunits that do admit a finite factorization into irreducibles....

### Boundary map and overrings of half-factorial domains

Bollettino dell'Unione Matematica Italiana

We investigate factorization of elements in overrings of a half-factorial domain $A$ in relation with the behaviour of the boundary map of $A$. It turns out that a condition, called ${\mathcal{C}}^{\star }$, on the extension plays a central role in this study. We finally apply our results to the special case of $A+XB\left[X\right]$ polynomial rings.

### Class Groups of Localities of Rings of Invariants of Reductive Algebraic Groups.

Mathematische Zeitschrift

### Complete local factorial rings which are not Cohen-Macaulay in characteristic $p$

Annales scientifiques de l'École Normale Supérieure

Kybernetika

### Division et composition dans l'anneau des séries de Dirichlet analytiques

Annales de l'Institut Fourier

Ce travail est une étude analytique locale de l’anneau des séries de Dirichlet convergentes. Dans un premier temps, on établit des propriétés arithmétiques de cet anneau ; on prouve en particulier sa factorialité, que l’on déduit de théorèmes de division du type Weierstrass. Ensuite, on s’intéresse à des problèmes de composition. Soient $f\left(s\right)$ et $\varphi \left(s\right)$ des séries de Dirichlet convergentes. On sait que $f\left({c}_{0}s+\varphi \left(s\right)\right),$ avec ${c}_{0}\in {ℕ}^{*},$ est encore une série de Dirichlet convergente. On étudie la réciproque : sous les hypothèses que...

### Divisors on Varieties of Complexes.

Mathematische Annalen

### Elasticity of A + XB[X] when A ⊂ B is a minimal extension of integral domains

Colloquium Mathematicae

We investigate the elasticity of atomic domains of the form ℜ = A + XB[X], where X is an indeterminate, A is a local domain that is not a field, and A ⊂ B is a minimal extension of integral domains. We provide the exact value of the elasticity of ℜ in all cases depending the position of the maximal ideals of B. Then we investigate when such domains are half-factorial domains.

### Equivalent Conditions for Unique Factorization

Publications du Département de mathématiques (Lyon)

### Essentially indecomposable modules over a complete discrete valuation ring

Rendiconti del Seminario Matematico della Università di Padova

### Exponential Automorphisms of Complete Local Rings.

Mathematische Zeitschrift

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