scholarly journals Prime t-ideals in power series rings over a discrete valuation domain

2010 ◽  
Vol 324 (12) ◽  
pp. 3401-3407 ◽  
Author(s):  
Mi Hee Park
Keyword(s):  
Power Series ◽  
Valuation Domain ◽  
Discrete Valuation Domain ◽  
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.

Some results concerning the local analytic branches of an algebraic variety

1953 ◽  
Vol 49 (3) ◽  
pp. 386-396 ◽  
Author(s):  
D. G. Northcott
Keyword(s):  
Algebraic Geometry ◽  
Power Series ◽  
Algebraic Variety ◽  
Recent Progress ◽  
Rapid Development ◽  
Noetherian Rings ◽  
Local Rings ◽  
Power Series Rings ◽  
Analytic Algebra ◽  
Topological Theories

The recent progress of modern algebra in analysing, from the algebraic standpoint, the foundations of algebraic geometry, has been marked by the rapid development of what may be called ‘analytic algebra’. By this we mean the topological theories of Noetherian rings that arise when one uses ideals to define neighbourhoods; this includes, for instance, the theory of power-series rings and of local rings. In the present paper some applications are made of this kind of algebra to some problems connected with the notion of a branch of a variety at a point.

Cyclic codes over formal power series rings

2011 ◽  
Vol 31 (1) ◽  
pp. 331-343 ◽  
Author(s):  
Steven T. Dougherty ◽  
Liu Hongwei
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Cyclic Codes ◽  
Power Series Rings ◽  
Formal Power
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