Abstract
All rings considered in this paper are commutative, with identity and ring-homomorphisms are unital. If R is a ring, then dim(R) denotes the Krull dimension of R, that is the supremum of lengths of chains of prime ideals of R. A domain D is said to have valuative dimension n (in short, dim v (D) = n) if each valuation overring of D has dimension at most n and there exists a valuation overring of D of dimension n. If no such integer n exists, D is said to have infinite valuative dimension [11]. For nondomains, dim v (R) = sup dim v (R/P) : P ∈ Spec(R). Recall further that a finite-dimensional domain D is a Jaffard domain if dim v (D) = dim, (D). As the class of Jaffard domains is not stable under localization, a domain D is defined to be a locally Jaffard domain if D P is a Jaffard domain for each prime ideal P of D (cf. [1]).
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Supported by Consiglio Nazionale delle Ricerche and Terza Università degli Studi di Roma.
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Girolami, F., Kabbaj, SE. (1995). The Dimension of the Tensor Product of Two Particular Pullbacks. In: Facchini, A., Menini, C. (eds) Abelian Groups and Modules. Mathematics and Its Applications, vol 343. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0443-2_17
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DOI: https://doi.org/10.1007/978-94-011-0443-2_17
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