References
- Cohn, P. M. (1954). An invariant characterization of pseudo-valuations. Math. Proc. Camb. Phil. Soc. 50(2):159–177. DOI: 10.1017/S0305004100029200.
- Endler, O. (1972). Valuation Theory. New York, NY: Springer-Verlag.
- Fornasiero, A., Kuhlmann, F. V., Kuhlmann, S. (2010). Towers of complements to valuation rings and truncation closed embeddings of valued fields. J. Algebra 323(3):574–600. DOI: 10.1016/j.jalgebra.2009.11.023.
- Huckaba, J. A. (1969). Extensions of pseudo-valuations. Pacific J. Math. 29(2):295–302. DOI: 10.2140/pjm.1969.29.295.
- Kaplansky, I. (1974). Commutative Rings. Rev. ed. Chicago, IL: University of Chicago Press.
- Kang, B. G., Oh, D. Y. (1998). Lifting up an infinite chain of prime ideals to a valuation ring. Proc. Amer. Math. Soc. 126(03):645–646.
- Knebusch, M., Zhang, D. (2002). Manis Valuations and Prüfer Extensions. Berlin, Germany: Springer-Verlag.
- Mahadavi-Hezavehi, M. (2002). Matrix pseudo-valuations on rings and their associated skew fields. Int. Math. J. 2(1):7–30.
- Mathiak, K. (1986). Valuations of Skew Fields and Projective Hjelmslev Spaces. Lecture Notes in Mathematics, Vol. 1175. Berlin, Germany: Springer.
- Morandi, P. J. (1989). Value functions on central simple algebras. Trans. Amer. Math. Soc. 315(2):605–622. DOI: 10.2307/2001297.
- Oystaeyen, F. V., Verschoren, A. (1981). Non-Commutative Algebraic Geometry, LNM 887. Berlin, Germany: Springer-Verlag.
- Reiner, I. (1975). Maximal Orders. London Mathematical Society Monographs, Vol. 5. London, NY: Academic Press, p. 395.
- Sarussi, S. (2012). Quasi-valuations extending a valuation. J. Algebra 372:318–364. DOI: 10.1016/j.jalgebra.2012.09.019.
- Sarussi, S. (2019). Quasi-valuations and algebras over valuation domains. Commun. Algebra http://arxiv.org/abs/1308.4743. DOI: 10.1080/00927872.2018.1522322.
- Sarussi, S. (2017). Maximal covers of chains of prime ideals. Beiträge zur Algebra und Geometrie/Contributions to Algebra and Geometry 58(3):483–498. DOI: 10.1007/s13366-017-0331-0
- Tignol, J.-P., Wadsworth, A. R. (2009). Value functions and associated graded rings for semisimple algebras. Trans. Amer. Math. Soc. 362(02):687–726. DOI: 10.1090/S0002-9947-09-04681-9.
- Wadsworth, A. R. (2002). Valuation theory on finite dimensional division algebras. In: Kuhlmann, F.-V., ed. Valuation Theory and Its Applications. Fields Institute Communications 32, Vol. 1. Providence, RI: American Mathematical Society.
- Wehrung, F. (1996). Monoids of intervals of ordered abelian groups. J. Algebra 182(1):287–328. DOI: 10.1006/jabr.1996.0172.