Specialization chains of real valuation rings (Q923651)

The author proves here the existence of specialization chains of real valuation rings with prescribed centers, ranks, dimensions and value groups. This is a complete solution of a problem, partially solved in the author's Ph. D. thesis. The proof is obtained by rather elementary algebraic methods; in particular without using Hironaka's desingularization theorem, which was the basic tool for Bröcker and Schülting to obtain a similar result [\textit{L. Bröcker} and \textit{H. W. Schülting}, J. Reine Angew. Math. 365, 12-32 (1986; Zbl 0577.12021)]. Statements are in the language of real spectrum.