Results 191 to 200 of about 19,103 (226)

Composition rings from formal power series rings

Communications in Algebra, 2017
ABSTRACTWe study the ideals in some Dickson nearrings of polynomials and formal power series. For some of their related quotients, we introduce variants and generalizations, and construct compositi...
Gallina, Giordano, Morini, Fiorenza
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On the solutions of the translation equation in rings of formal power series

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 2005
For \(\mathbb{K}\in\{\mathbb{R},\mathbb{C}\}\) let \(\mathbb{K}[[X]]\) denote the ring of formal power series with coefficients from \(\mathbb{K}\) and let \(\Gamma(\mathbb{K})\) denote the group of invertible power series. \(L^1_{\infty}\) is the group consisting of all sequences \((x_1,x_2,\ldots)\in\mathbb{K}^{\infty}\) such that \(x_1\neq 0\) with ...
Jabloński, Wojciech, Reich, Ludwig
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Rings of Formal Power Series

Canadian Mathematical Bulletin, 1971
In this brief exposition we collect several results on rings of formal power series with coefficients from a field or a ring with some special properties. The results that are catalogued below are mostly algebraic in nature.
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t-closed rings of formal power series

Archiv der Mathematik, 1999
Let \(A \subset B\) be rings. \(A\) is said to be \(t\)-closed in \(B\) if for each \(a \in A\) and \(b \in B\) such that \(b^{2}-ab, b^{3}-ab^{2} \in A\) then \(b \in A\). In this note, the author proves that if \(A\) and \(B\) satisfy that for each \(a \in A\) and \(b \in B\) such that \(ab \in A\) then \(ab^{2} \in A\) and that \(A\) is \(t\)-closed
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On the bandwidth dimension of the ring of formal power series

Russian Mathematical Surveys, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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Cyclic codes over formal power series rings

Acta Mathematica Scientia, 2011
Abstract In this article, cyclic codes and negacyclic codes over formal power series rings are studied. The structure of cyclic codes over this class of rings is given, and the relationship between these codes and cyclic codes over finite chain rings is obtained. Using an isomorphism between cyclic and negacyclic codes over formal power series rings,
Steven T. Dougherty, Liu Hongwei
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