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Cyclic codes over formal power series rings
Acta Mathematica Scientia, 2011Abstract 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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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, 1986Let 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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Algebraic elements in formal power series rings
Israel Journal of Mathematics, 1988Let k be a perfect field of characteristic p. A set A of additive endomorphisms of k((x)) is defined such that an element f of k((x)) is algebraic over k(x) if and only if f is contained in an A-stable finite- dimensional k-vectorsubspace of k((x)). Other known characterizations of algebraicity are derived from this.
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Rings of formal power series and symmetric real semigroups
Journal of AlgebrazbMATH Open Web Interface contents unavailable due to conflicting licenses.
M. Dickmann, A. Petrovich
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Rings of formal power series with homeomorphic prime spectra
Rendiconti del Circolo Matematico di Palermo, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Rings of Formal Power Series in an Infinite Set of Indeterminates
Communications in Algebra, 2014Let 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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Formal Power Series Over Strongly Hopfian Rings
Communications in Algebra, 2010A commutative ring R is said to be strongly Hopfian if the chain of annihilators ann(a) ⊆ ann(a 2) ⊆ … stabilizes for each a ∈ R. In this article, we are interested in the class of strongly Hopfian rings and the transfer of this property from a commutative ring R to the ring of the power series R[[X]]. We provide an example of a strongly Hopfian ring R
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ON THE FIBRE RINGS OF A FORMAL POWER SERIES EXTENSION
The Quarterly Journal of Mathematics, 1977openaire +1 more source