Displaying similar documents to “Unique factorization in non-atomic integral domains”

Star-invertible ideals of integral domains

Gyu Whan Chang, Jeanam Park (2003)

Bollettino dell'Unione Matematica Italiana

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Let ∗ be a star-operation on R and ∗ s the finite character star-operation induced by ∗ . The purpose of this paper is to study when ∗ = v or ∗ s = t . In particular, we prove that if every prime ideal of R is ∗ -invertible, then ∗ = v , and that if R is a unique ∗ -factorable domain, then R is a Krull domain.

Pseudo-valuation rings. II

David F. Anderson, Ayman Badawi, David E. Dobbs (2000)

Bollettino dell'Unione Matematica Italiana

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Viene data una condizione sufficiente affinchè un sopra-anello di un anello di pseudo-valutazione (PVR) sia ancora un PVR. Da ciò segue che se R , M è un PVR, allora ogni sopra-anello di R è un PVR se (e soltanto se) R ⁢ u è quasi-locale per ciascun elemento u di M : M . Vari risultati sono dimostrati per un ideale primo di un anello commutativo arbitrario R , avente Z ⁢ R come insieme di zero-divisori. Per esempio, se P è un primo «forte» di R e contiene un elemento non-zero divisore di R , allora P : P è...

Fixed-place ideals in commutative rings

Ali Rezaei Aliabad, Mehdi Badie (2013)

Commentationes Mathematicae Universitatis Carolinae

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Let I be a semi-prime ideal. Then P ∘ ∈ Min ( I ) is called irredundant with respect to I if I ≠ ⋂ P ∘ ≠ P ∈ Min ( I ) P . If I is the intersection of all irredundant ideals with respect to I , it is called a fixed-place ideal. If there are no irredundant ideals with respect to I , it is called an anti fixed-place ideal. We show that each semi-prime ideal has a unique representation as an intersection of a fixed-place ideal and an anti fixed-place ideal. We say the point p ∈ β X is a fixed-place point if O p ( X ) is a fixed-place ideal. In...

On nonregular ideals and z ∘ -ideals in C ( X )

F. Azarpanah, M. Karavan (2005)

Czechoslovak Mathematical Journal

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The spaces X in which every prime z ∘ -ideal of C ( X ) is either minimal or maximal are characterized. By this characterization, it turns out that for a large class of topological spaces X , such as metric spaces, basically disconnected spaces and one-point compactifications of discrete spaces, every prime z ∘ -ideal in C ( X ) is either minimal or maximal. We will also answer the following questions: When is every nonregular prime ideal in C ( X ) a z ∘ -ideal? When is every nonregular (prime) z -ideal in C ( X ) a...