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### Semirigid GCD Domains.

Manuscripta mathematica

### A General Theory of Almost Factoriality.

Manuscripta mathematica

### On Finite Conductor Domains.

Manuscripta mathematica

### On Riesz groups.

Manuscripta mathematica

### On some class groups of an integral domain

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

### The Schreier Property and Gauss' Lemma

Bollettino dell'Unione Matematica Italiana

Let $D$ be an integral domain with quotient field $D$. Recall that $D$ is Schreier if $D$ is integrally closed and for all $x,y,z\in D\setminus\{0\}$, $x|yz$ implies that $x=r\cdot s$ where $r|y$ e $s|z$. A GCD domain is Schreier. We show that an integral domain $D$ is a GCD domain if and only if (i) for each pair $a,b\in D\setminus\{0\}$, there is a finitely generated ideal $B$ such that $aD\bigcap bD=B_{v}$ and (ii) every quadratic in $D[X]$ that is a product of two linear polynomials in $K[X]$ is a product of two linear polynomials in $D[X]$. We also show that $D$ is Schreier if and only if every polynomial...

### Star operations in extensions of integral domains

Actes des rencontres du CIRM

An extension $D\subseteq R$ of integral domains is $t$- (resp., $t$-) if ${\left(IR\right)}^{-1}={\left({I}^{-1}R\right)}_{v}$ (resp., ${\left(IR\right)}_{v}={\left({I}_{v}R\right)}_{v}\right)$ for every nonzero finitely generated fractional ideal $I$ of $D$. We show that strongly $t$-compatible implies $t$-compatible and give examples to show that the converse does not hold. We also indicate situations where strong $t$-compatibility and its variants show up naturally. In addition, we study integral domains $D$ such that $D\subseteq R$ is strongly $t$-compatible (resp., $t$-compatible) for every overring $R$ of $D$.

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

International Journal of Mathematics and Mathematical Sciences

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