1 |
P. R. Halmos, Naive Set Theory, Springer-Verlag, New York-Heidelberg, 1974.
|
2 |
N. Popescu and A. Zaharescu, On the structure of the irreducible polynomials over local fields, J. Number Theory 52 (1995), no. 1, 98-118. https://doi.org/10.1006/jnth.1995.1058
DOI
|
3 |
S. Warner, Topological Fields, Mathematics Studies, vol. 157, North Holland, Amsterdam, 1989.
|
4 |
K. Aghigh and S. K. Khanduja, On the main invariant of elements algebraic over a Henselian valued field, Proc. Edinb. Math. Soc. (2) 45 (2002), no. 1, 219-227. https://doi.org/10.1017/S0013091500000936
DOI
|
5 |
K. Aghigh and S. K. Khanduja, On chains associated with elements algebraic over a Henselian valued field, Algebra Colloq. 12 (2005), no. 4, 607-616. https://doi.org/10.1142/S100538670500057X
DOI
|
6 |
K. Aghigh and A. Nikseresht, Characterizing distinguished pairs by using liftings of irreducible polynomials, Canad. Math. Bull. 58 (2015), no. 2, 225-232. https://doi.org/10.4153/CMB-2014-064-2
DOI
|
7 |
K. Aghigh and A. Nikseresht, Constructing complete distinguished chains with given invariants, J. Algebra Appl. 14 (2015), no. 3, 1550026, 10 pp. https://doi.org/10.1142/S0219498815500267
DOI
|
8 |
V. Alexandru, N. Popescu, and Al. Zaharescu, Minimal pairs of definition of a residual transcendental extension of a valuation, J. Math. Kyoto Univ. 30 (1990), no. 2, 207-225. https://doi.org/10.1215/kjm/1250520067
DOI
|
9 |
O. Endler, Valuation Theory, Berlin-Heidelberg, Springer Verlag, 1972.
|
10 |
F. -V. Kuhlmann, A classification of Artin-Schreier defect extensions and characterizations of defectless fields, Illinois J. Math. 54 (2010), no. 2, 397-448. http://projecteuclid.org/euclid.ijm/1318598666
|
11 |
A. Bishnoi and S. K. Khanduja, On algebraically maximal valued fields and defectless extensions, Canad. Math. Bull. 55 (2012), no. 2, 233-241. https://doi.org/10.4153/CMB-2011-148-0
DOI
|
12 |
F. -V. Kuhlmann, Valuation Theory of Fields, Abelian Groups and Modules, Monograph in preparation, Preliminary versions of several chapters are available on the web site https://math.usask.ca/~fvk/Fvkbook.htm
|
13 |
S. Anscombe and F.-V. Kuhlmann, Notes on extremal and tame valued fields, J. Symb. Log. 81 (2016), no. 2, 400-416. https://doi.org/10.1017/jsl.2015.62
DOI
|
14 |
S. Bhatia and S. K. Khanduja, On limits of sequences of algebraic elements over a complete field, Algebra Colloq. 12 (2005), no. 4, 617-628. https://doi.org/10.1142/S1005386705000581
DOI
|
15 |
S. K. Khanduja, N. Popescu, and K. W. Roggenkamp, On minimal pairs and residually transcendental extensions of valuations, Mathematika 49 (2002), no. 1-2, 93-106. https://doi.org/10.1112/S0025579300016090
DOI
|
16 |
R. Brown and J. L. Merzel, The main invariant of a defectless polynomial, J. Algebra Appl. 12 (2013), no. 1, 1250122, 16 pp. https://doi.org/10.1142/S0219498812501228
DOI
|
17 |
F. Delon, Quelques proprietes des corps valu'es en theories des modeles, These Paris VII, 1981.
|
18 |
S. K. Khanduja and R. Khassa, On invariants and strict systems of irreducible polynomials over Henselian valued fields, Comm. Algebra 39 (2011), no. 2, 584-593. https://doi.org/10.1080/00927871003591934
DOI
|
19 |
F. -V. Kuhlmann, The defect, in Commutative algebra-Noetherian and non-Noetherian perspectives, 277-318, Springer, New York, 2011. https://doi.org/10.1007/978-1-4419-6990-3_11
DOI
|
20 |
R. Brown and J. L. Merzel, Invariants of defectless irreducible polynomials, J. Algebra Appl. 9 (2010), no. 4, 603-631. https://doi.org/10.1142/S0219498810004130
DOI
|
21 |
A. Dutta, On the non-uniqueness of maximal purely wild extensions, submitted, 2020, arXiv:2011.09310.
|
22 |
A. J. Engler and A. Prestel, Valued Fields, Springer-Verlag, Berlin, 2005.
|
23 |
S. K. Khanduja, On Brown's constant associated with irreducible polynomials over Henselian valued fields, J. Pure Appl. Algebra 214 (2010), no. 12, 2294-2300. https://doi.org/10.1016/j.jpaa.2010.02.028
DOI
|
24 |
F. -V. Kuhlmann, The algebra and model theory of tame valued fields, J. Reine Angew. Math. 719 (2016), 1-43. https://doi.org/10.1515/crelle-2014-0029
DOI
|
25 |
N. Moraes de Oliveira and E. Nart, Defectless polynomials over henselian fields and inductive valuations, J. Algebra 541 (2020), 270-307. https://doi.org/10.1016/j.jalgebra.2019.08.033
DOI
|
26 |
S. K. Khanduja and J. Saha, A generalized fundamental principle, Mathematika 46 (1999), no. 1, 83-92. https://doi.org/10.1112/S0025579300007580
DOI
|
27 |
F.-V. Kuhlmann, M. Pank, and P. Roquette, Immediate and purely wild extensions of valued fields, Manuscripta Math. 55 (1986), no. 1, 39-67. https://doi.org/10.1007/BF01168612
DOI
|
28 |
N. Bourbaki, Theory of Sets, Elements of Mathematics (Berlin), Springer-Verlag, Berlin, 2004. https://doi.org/10.1007/978-3-642-59309-3
DOI
|