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Star operations in extensions of integral domains

David F. Anderson, Said El Baghdadi, Muhammad Zafrullah (2010)

Actes des rencontres du CIRM

An extension D ⊆ R of integral domains is strongly t -compatible (resp., t -compatible) if ( I R ) - 1 = ( I - 1 R ) v (resp., ( I R ) v = ( I v R ) v ) 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 ⊆ R is strongly t -compatible (resp., t -compatible) for every overring R of D .

Star-invertible ideals of integral domains

Gyu Whan Chang, Jeanam Park (2003)

Bollettino dell'Unione Matematica Italiana

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.

Strongly fixed ideals in C ( L ) and compact frames

A. A. Estaji, A. Karimi Feizabadi, M. Abedi (2015)

Archivum Mathematicum

Let C ( L ) be the ring of real-valued continuous functions on a frame L . In this paper, strongly fixed ideals and characterization of maximal ideals of C ( L ) which is used with strongly fixed are introduced. In the case of weakly spatial frames this characterization is equivalent to the compactness of frames. Besides, the relation of the two concepts, fixed and strongly fixed ideals of C ( L ) , is studied particularly in the case of weakly spatial frames. The concept of weakly spatiality is actually weaker than...

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