scholarly journals Krull dimension of power series rings over a globalized pseudo-valuation domain

2010 ◽  
Vol 214 (6) ◽  
pp. 862-866 ◽  
Author(s):  
Mi Hee Park
Keyword(s):  
Power Series ◽  
Krull Dimension ◽  
Valuation Domain ◽  
Power Series Rings

Krull dimension of power series rings

2020 ◽  
Vol 562 ◽  
pp. 306-322
Author(s):  
Phan Thanh Toan ◽  
Byung Gyun Kang
Keyword(s):  
Power Series ◽  
Krull Dimension ◽  
Power Series Rings

CONSTRUCTING CHAINS OF PRIMES IN POWER SERIES RINGS, II

2012 ◽  
Vol 12 (01) ◽  
pp. 1250123 ◽  
Author(s):  
K. ALAN LOPER ◽  
THOMAS G. LUCAS
Keyword(s):  
Lower Bound ◽  
Power Series ◽  
Polynomial Ring ◽  
Integral Domain ◽  
Valuation Domain ◽  
Main Concern ◽  
Power Series Ring ◽  
One Dimensional ◽  
Series Ring ◽  
Power Series Rings

For an integral domain D of dimension n, the dimension of the polynomial ring D[ x ] is known to be bounded by n + 1 and 2n + 1. While n + 1 is a lower bound for the dimension of the power series ring D[[ x ]], it often happens that D[[ x ]] has infinite chains of primes. For example, such chains exist if D is either an almost Dedekind domain that is not Dedekind or a one-dimensional nondiscrete valuation domain. The main concern here is in developing a scheme by which such chains can be constructed in the gap between MV[[ x ]] and M[[ x ]] when V is a one-dimensional nondiscrete valuation domain with maximal ideal M. A consequence of these constructions is that there are chains of primes similar to the set of ω1 transfinite sequences of 0's and 1's ordered lexicographically.

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