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Some remarks on the altitude inequality

Noômen Jarboui (1999)

Colloquium Mathematicae

We introduce and study a new class of ring extensions based on a new formula involving the heights of their primes. We compare them with the classical altitude inequality and altitude formula, and we give another characterization of locally Jaffard domains, and domains satisfying absolutely the altitude inequality (resp., the altitude formula). Then we study the extensions R ⊆ S where R satisfies the corresponding condition with respect to S (Definition 3.1). This leads to a new characterization...

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 .

Sur les Extensions Triviales Commutatives

Farid Kourki (2009)

Annales mathématiques Blaise Pascal

Nous caractérisons les extensions triviales semiGoldie, de cogénération finie, mininjectives et quasi-Frobeniusiens. Comme application, nous montrons que tout anneau noethérien s’injecte dans un anneau quasi-Frobeniusien.

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