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 of integral extensions.
@article{bwmeta1.element.bwnjournal-article-cmv80i1p39bwm,
author = {No\^omen Jarboui},
title = {Some remarks on the altitude inequality},
journal = {Colloquium Mathematicae},
volume = {79},
year = {1999},
pages = {39-52},
zbl = {0972.13009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv80i1p39bwm}
}
Jarboui, Noômen. Some remarks on the altitude inequality. Colloquium Mathematicae, Tome 79 (1999) pp. 39-52. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv80i1p39bwm/
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