Formal and Convergent Power Series Rings

2004 ◽  
pp. 143-168
Author(s):  
K. Kiyek ◽  
J. L. Vicente
Keyword(s):  
Power Series ◽  
Convergent Power Series ◽  
Power Series Rings

Joseph Becker and Leonard Lipshitz. Remarks on the elementary theories of formal and convergent power series. Fundament a mathematicae, vol. 105 (1980), pp. 229–239. - Françoise Delon. Indécidabilité de la théorie des anneaux de séries formelles à plusiers indéterminées. Fundament a mathematicae, vol. 112 (1981), pp. 215–229. - J. Becker, J. Denef, and L. Lipshitz. Further remarks on the elementary theory of formal power series rings. Model theory of algebra and arithmetic, Proceedings of the Conference on Applications of Logic to Algebra and Arithmetic held at Karpacz, Poland, September 1–7, 1979, edited by L. Pacholski, J. Wierzejewski, and A. J. Wilkie, Lecture notes in mathematics, vol. 834, Springer-Verlag, Berlin, Heidelberg, and New York, 1980, pp. 1–9. - Françoise Delon. Hensel fields in equal characteristic p > 0. Model theory of algebra and arithmetic, Proceedings of the Conference on Applications of Logic to Algebra and Arithmetic held at Karpacz, Poland, September 1–7, 1979, edited by L. Pacholski, J. Wierzejewski, and A. J. Wilkie, Lecture notes in mathematics, vol. 834, Springer-Verlag, Berlin, Heidelberg, and New York, 1980, pp. 108–116.

1985 ◽  
Vol 50 (3) ◽  
pp. 853-854
Author(s):  
S. Basarab
Keyword(s):  
New York ◽  
Power Series ◽  
Model Theory ◽  
Elementary Theory ◽  
Convergent Power Series ◽  
Characteristic P ◽  
Lecture Notes ◽  
Power Series Rings ◽  
Formal Power ◽  
Elementary Theories

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

scholarly journals Constructing chains of primes in power series rings

2011 ◽  
Vol 334 (1) ◽  
pp. 175-194 ◽  
Author(s):  
K. Alan Loper ◽  
Thomas G. Lucas
Keyword(s):  
Power Series ◽  
Power Series Rings

How to Construct Huge Chains of Prime Ideals in Power Series Rings

2014 ◽  
pp. 225-238 ◽  
Author(s):  
Byung Gyun Kang ◽  
Phan Thanh Toan
Keyword(s):  
Power Series ◽  
Prime Ideals ◽  
Power Series Rings

Polynomial and power series rings

2018 ◽  
pp. 54-75
Author(s):  
Karlheinz Spindler
Keyword(s):  
Power Series ◽  
Power Series Rings

On Ore extension and skew power series rings with some restrictions on zero-divisors

2016 ◽  
Vol 16 (09) ◽  
pp. 1750164
Author(s):  
E. Hashemi ◽  
A. As. Estaji ◽  
A. Alhevaz
Keyword(s):  
Power Series ◽  
Left Zero ◽  
Ore Extension ◽  
Series Ring ◽  
Zero Divisors ◽  
Open Questions ◽  
Ore Extensions ◽  
Power Series Rings ◽  
Extension Ring ◽  
The Right

The study of rings with right Property ([Formula: see text]), has done an important role in noncommutative ring theory. Following literature, a ring [Formula: see text] has right Property ([Formula: see text]) if every finitely generated two-sided ideal consisting entirely of left zero-divisors has a nonzero right annihilator. Our results in this paper concerns the right Property ([Formula: see text]) of Ore extensions as well as skew power series rings. We will show that if [Formula: see text] is a right duo ring, then the skew power series ring [Formula: see text] has right Property ([Formula: see text]), when [Formula: see text] is right Noetherian and [Formula: see text]-compatible. Moreover, for a right duo ring [Formula: see text] which is [Formula: see text]-compatible, it is shown that (i) the Ore extension ring [Formula: see text] has right Property ([Formula: see text]) and (ii) [Formula: see text] is right zip if and only if [Formula: see text] is right zip. As a corollary of our results, we provide answers to some open questions related to Property [Formula: see text], raised in [C. Y. Hong, N. K. Kim, Y. Lee and S. J. Ryu, Rings with Property ([Formula: see text]) and their extensions, J. Algebra 315 (2007) 612–628].

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