References

TOTAL VALUATION RINGS IN


[1] H. H. Brungs and M. Schöder, Valuation rings in Ore extensions, J. Algebra 235(2) (2001), 665-680.
DOI: https://doi.org/10.1006/jabr.2000.8484

[2] S. Kobayashi, H. Marubayashi, N. Popescu and C. Vraciu, Total valuation rings of containing K, Com. Algebra 30(11) (2002), 5535-5546.

[3] H. Marubayashi, H. Miyamoto and A. Ueda, Noncommutative valuation rings and semi-hereditary orders, K-Monographs in Math.3, Kluwer Academic Publishers, 1997.

[4] A. R. Wadsworth, Dubrovin valuation rings and Henselization, Math. Ann. 283 (1989), 301-328.
DOI: https://doi.org/10.1007/BF01446437

[5] G. Xie, Y. Chen, H. Marubayashi and Y. Wang, A new classification of graded extensions in a skew Laurent polynomial ring, Far East J. Math. Sci. (FJMS) 40(1) (2010), 37-44.

[6] G. Xie, S. Kobayashi, H. Marubayashi, N. Popescu and C. Vraciu, Noncommutative valuation rings of the quotient Artinian ring of a skew polynomial ring, Algebra. Represent. Theory 8 (2005), 57-68.
DOI: https://doi.org/10.1007/s10468-004-5766-y

[7] G. Xie, J. Liang and M. Wang, Quotient skew fields of skew group rings of torsion free additive groups over a skew field (to appear in FJMS).

[8] H. Marubayashi and G. Xie, A classification of graded extensions in a skew Laurent polynomial ring, J. Math. Soc. Japan 60(2) (2008), 423-443.
DOI: https://doi.org/10.2969/jmsj/06020423

[9] H. Marubayashi and G. Xie, A classification of graded extensions in a skew Laurent polynomial ring, II, J. Math. Soc. Japan 61(4) (2009), 1111-1130.

[10] G. Xie, M. Wang and J. Liang, Graded extensions in (Preprint).