Open Access
Issue |
ITM Web Conf.
Volume 20, 2018
International Conference on Mathematics (ICM 2018) Recent Advances in Algebra, Numerical Analysis, Applied Analysis and Statistics
|
|
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Article Number | 01002 | |
Number of page(s) | 9 | |
Section | Algebra | |
DOI | https://doi.org/10.1051/itmconf/20182001002 | |
Published online | 12 October 2018 |
- J.T. Arnold, Krull dimension in power series rings, Trans. Amer. Math. Soc. 177, 299– 304 (1973). [CrossRef] [Google Scholar]
- J.T. Arnold and D.W. Boyd, Transcendence degree in power series rings, J. Algebra 57, no. 1, 180–195 (1979). [CrossRef] [Google Scholar]
- J.W. Brewer, Power series over commutative rings, Lecture Notes in Pure Appl. Math. 64, (Marcel Dekker, Inc., New York, 1981). [Google Scholar]
- R. Gilbert, A note on the quotient field of the domain D[[X]], Proc. Amer. Math. Soc. 18, 1138–1140 (1967). [CrossRef] [Google Scholar]
- L. Gillman and M. Jerison, Rings of continuous functions, (The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960). [CrossRef] [Google Scholar]
- R. Gilmer, Multiplicative ideal theory, (Marcel Dekker, New York, 1972). [Google Scholar]
- R. Gilmer, On commutative rings of finite rank, Duke Math. J. 39, 381–383 (1972). [CrossRef] [Google Scholar]
- L.T.N. Giau and P.T. Toan, Transcendental Degree in Power Series Rings, J. Algebra 501, 51–67 (2018). [CrossRef] [Google Scholar]
- B.G. Kang and M.H. Park, Krull-dimension of the power series ring over a nondiscretevaluation domain is uncountable, J. Algebra 378, 12–21 (2013). [CrossRef] [Google Scholar]
- B.G. Kang and P.T. Toan, A remark on the Noetherian property of power series rings Pacific J. Math. 283, 353–363 (2016). [Google Scholar]
- B.G. Kang and P.T. Toan, Krull dimension of power series rings over non-SFT domains, J. Algebra 499, 516–537 (2018). [CrossRef] [Google Scholar]
- B.G. Kang and P.T. Toan, Krull dimension of a power series ring over a valuation domain, preprint. [Google Scholar]
- I. Kaplansky, Commutative rings, Revised edition, (The University of Chicago Press, Chicago, Ill.-London, 1974). [Google Scholar]
- K.A. Loper and T.G. Lucas, Constructing chains of primes in power series rings, J. Algebra 334, 175–194 (2011). [CrossRef] [Google Scholar]
- K.A. Loper and T.G. Lucas, Constructing chains of primes in power series rings II, J. Algebra Appl. 12, no. 1, 1250123, 30 pp. (2013). [CrossRef] [Google Scholar]
- A. Seidenberg, A note on the dimension theory of rings, Pacific J. Math. 3, 505–512 (1953). [CrossRef] [Google Scholar]
- A. Seidenberg, On the dimension theory of rings II, Pacific J. Math. 4, 603–614 (1954). [CrossRef] [Google Scholar]
- P.B. Sheldon, How changing D[[X]] changes its quotient field, Trans. Amer. Math. Soc. 159, 223–244 (1971). [Google Scholar]
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