Results 191 to 200 of about 7,928 (214)

On the bandwidth dimension of the ring of formal power series

Russian Mathematical Surveys, 2001
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Arithmetic in the Ring of Formal Power Series with Integer Coefficients

The American Mathematical Monthly, 2008
of polynomials R[x] over R, namely the ring ^[[x]] of formal powers series in one variable over R, is hardly ever mentioned in such a course. In most cases, it is relegated to the homework problems (or to the exercises in the textbooks), and one learns that, like R[x], R[[x]] is an integral domain provided that R is an integral domain.
Daniel Birmajer, Juan B. Gil
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Principal quasi-Baerness of formal power series rings

Acta Mathematica Sinica, English Series, 2010
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Liu, Zhong Kui, Zhang, Wen Hui
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Formal and Convergent Power Series Rings

2004
In this chapter we prepare the ground for the proof of the Jung-Abhyankar theorem in section 2 and the study of quasiordinary power series in section 4 of chapter V. We assume that the reader is acquainted with the notion of power series over a field; in section 1, for the convenience of the reader, we give some background, introduce convergent power ...
K. Kiyek, J. L. Vicente
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Nonnil-Noetherian Rings and Formal Power Series

Algebra Colloquium, 2020
Let A be a commutative ring with unit. We characterize when A is nonnil-Noetherian in terms of the quotient ring A/ Nil(A) and in terms of the power series ring A[[X]].
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Algebraic elements in formal power series rings II

Israel Journal of Mathematics, 1989
[For part I see ibid. 63, No.3, 281-288 (1988; Zbl 0675.13015).] One considers algebraic formal power series in several variables over a perfect field of characteristic \(p.\) Upper bounds are obtained for the degrees of their diagonals, Hadamard products and Lamperti products.
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A note on ordinal numbers and rings of formal power series

Archive for Mathematical Logic, 1994
In ``Ordinal numbers and the Hilbert basis theorem'' [J. Symb. Log. 53, No. 3, 961-974 (1988; Zbl 0661.03046)], \textit{S. G. Simpson} has shown that over \(\text{RCA}_ 0\), for any or all countable fields \(K\), a formal version of Hilbert basis theorem is equivalent to the assertion that the ordinal number \(\omega^ \omega\) is well ordered.
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A note on prime ideals in a formal power series ring

The science reports of the Kanazawa University＝金沢大学理科報告, 1986
Let V be a valuation domain and P a prime ideal of V. This paper investigates the question of when PV[[X]] is a prime ideal of V[[X]]. If P is principal or not countably generated, then \(PV[[X]]=P[[X]]\) and hence is prime. So we may suppose that P is countably generated (which is the case if V has only countably many primes).
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Rings of formal power series with homeomorphic prime spectra

Rendiconti del Circolo Matematico di Palermo, 1992
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Rings of Formal Power Series in an Infinite Set of Indeterminates

Communications in Algebra, 2014
Let α be an infinite cardinal number, Λ be an index set of cardinality > α, and {X λ}λ∈Λ be a set of indeterminates over an integral domain D. It is well known that there are three ways of defining the ring of formal power series in {X λ}λ∈Λ over D, say, D[[{X λ}]] i for i = 1, 2, 3. In this paper, we let D[[{X λ}]]α = ∪ {D[[{X λ}λ∈Γ]]3 | Γ ⊆ Λ and |Γ|
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