Ayache, Ahmed Some remakrs about chain conditions. (Quelques remarques sur les conditions de chaînes.) (French) Zbl 0989.13007 Arch. Math. 72, No. 4, 270-277 (1999). The most general version of the dimension inequality is established for arbitrary ring extensions. Then the rings satisfying the dimension formula are studied, along with the transfer of this property (and also universal catenarity) for integral extensions. Reviewer: Serban Raianu (Syracuse) MSC: 13C15 Dimension theory, depth, related commutative rings (catenary, etc.) 13B02 Extension theory of commutative rings 13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations 13G05 Integral domains Keywords:chain conditions; Krull dimension; catenary ring; dimension inequality; integral extensions PDFBibTeX XMLCite \textit{A. Ayache}, Arch. Math. 72, No. 4, 270--277 (1999; Zbl 0989.13007) Full Text: DOI