scholarly journals Some results on local cohomology of polynomial and formal power series rings: The one dimensional case

2016 ◽  
Vol 466 ◽  
pp. 184-194
Author(s):  
Pham Hung Quy
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Local Cohomology ◽  
Dimensional Case ◽  
One Dimensional ◽  
Power Series Rings ◽  
The One ◽  
Formal Power

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 Weighted kneading theory of one-dimensional maps with a hole

2004 ◽  
Vol 2004 (38) ◽  
pp. 2019-2038 ◽  
Author(s):  
J. Leonel Rocha ◽  
J. Sousa Ramos
Keyword(s):  
Hausdorff Dimension ◽  
Power Series ◽  
Formal Power Series ◽  
Topological Entropy ◽  
Escape Rate ◽  
One Dimensional ◽  
One Dimensional Maps ◽  
Formal Power ◽  
Kneading Theory

The purpose of this paper is to present a weighted kneading theory for one-dimensional maps with a hole. We consider extensions of the kneading theory of Milnor and Thurston to expanding discontinuous maps with a hole and introduce weights in the formal power series. This method allows us to derive techniques to compute explicitly the topological entropy, the Hausdorff dimension, and the escape rate.

Differential Completions and Differentially Simple Algebras

1989 ◽  
Vol 32 (3) ◽  
pp. 314-319
Author(s):  
Peter Seibt
Keyword(s):  
General Theory ◽  
Power Series ◽  
Formal Power Series ◽  
Power Series Rings ◽  
Simple Algebras ◽  
Formal Power

AbstractDifferentially simple local noetherian Q -algebras are shown to be always (a certain type of) subrings of formal power series rings. The result is established as an illustration of a general theory of differential filtrations and differential completions.

scholarly journals One-dimensional game of life and its growth functions

1992 ◽  
Vol 15 (3) ◽  
pp. 499-508
Author(s):  
Mohammad H. Ahmadi
Keyword(s):  
Power Series ◽  
Rational Function ◽  
Formal Power Series ◽  
Infinite Product ◽  
Growth Function ◽  
The Other ◽  
Arbitrary Integer ◽  
One Dimensional ◽  
Growth Functions ◽  
Formal Power

We start with finitely many1's and possibly some0's in between. Then each entry in the other rows is obtained from the Base2sum of the two numbers diagonally above it in the preceding row. We may formulate the game as follows: Defined1,jrecursively for1, a non-negative integer, andjan arbitrary integer by the rules:d0,j={1     for   j=0,k         (I)0   or   1   for   0<j<kd0,j=0   for   j<0   or   j>k              (II)di+1,j=di,j+1(mod2)   for   i≥0.      (III)Now, if we interpret the number of1's in rowias the coefficientaiof a formal power series, then we obtain a growth function,f(x)=∑i=0∞aixi. It is interesting that there are cases for which this growth function factors into an infinite product of polynomials. Furthermore, we shall show that this power series never represents a rational function.

A Note on z-Ideals and z°-Ideals of the Formal Power Series Rings and Polynomial Rings in an Infinite Set of Indeterminates

2020 ◽  
Vol 27 (03) ◽  
pp. 495-508
Author(s):  
Ahmed Maatallah ◽  
Ali Benhissi
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Cardinal Number ◽  
Prime Ideals ◽  
Infinite Cardinal ◽  
Series Ring ◽  
Formal Power Series Ring ◽  
Power Series Rings ◽  
Formal Power ◽  
Infinite Set

Let A be a ring. In this paper we generalize some results introduced by Aliabad and Mohamadian. We give a relation between the z-ideals of A and those of the formal power series rings in an infinite set of indeterminates over A. Consider A[[XΛ]]3 and its subrings A[[XΛ]]1, A[[XΛ]]2, and A[[XΛ]]α, where α is an infinite cardinal number. In fact, a z-ideal of the rings defined above is of the form I + (XΛ)i, where i = 1, 2, 3 or an infinite cardinal number and I is a z-ideal of A. In addition, we prove that the same condition given by Aliabad and Mohamadian can be used to get a relation between the minimal prime ideals of the ring of the formal power series in an infinite set of indeterminates and those of the ring of coefficients. As a natural result, we get a relation between the z°-ideals of the formal power series ring in an infinite set of indeterminates and those of the ring of coefficients.

scholarly journals A fresh look into monoid rings and formal power series rings

2019 ◽  
Vol 19 (01) ◽  
pp. 2050003
Author(s):  
Abolfazl Tarizadeh
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Universal Property ◽  
Polynomial Rings ◽  
Power Series Rings ◽  
Universal Properties ◽  
Ring Of Polynomials ◽  
Formal Power

In this paper, the ring of polynomials is studied in a systematic way through the theory of monoid rings. As a consequence, this study provides canonical approaches in order to find easy and rigorous proofs and methods for many facts on polynomials and formal power series; some of them as sample are treated in this paper. Besides the universal properties of the monoid rings and polynomial rings, a universal property for the formal power series rings is also established.

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