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Krull dimension in power series rings. (English) Zbl 0262.13007


MSC:

13J05 Power series rings
13C15 Dimension theory, depth, related commutative rings (catenary, etc.)
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References:

[1] J. T. Arnold and J. W. Brewer, When (\?[[\?]])_{\?[[\?]]} is a valuation ring, Proc. Amer. Math. Soc. 37 (1973), 326 – 332. · Zbl 0252.13008
[2] David E. Fields, Zero divisors and nilpotent elements in power series rings, Proc. Amer. Math. Soc. 27 (1971), 427 – 433. · Zbl 0219.13023
[3] David E. Fields, Dimension theory in power series rings, Pacific J. Math. 35 (1970), 601 – 611. · Zbl 0192.38701
[4] Robert W. Gilmer, Multiplicative ideal theory, Queen’s Papers in Pure and Applied Mathematics, No. 12, Queen’s University, Kingston, Ont., 1968. · Zbl 0155.36402
[5] Jack Ohm and R. L. Pendleton, Rings with noetherian spectrum, Duke Math. J. 35 (1968), 631 – 639. · Zbl 0172.32201
[6] A. Seidenberg, A note on the dimension theory of rings, Pacific J. Math. 3 (1953), 505 – 512. · Zbl 0052.26902
[7] A. Seidenberg, On the dimension theory of rings. II, Pacific J. Math. 4 (1954), 603 – 614. · Zbl 0057.26802
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