Results 141 to 150 of about 1,159 (179)

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
exaly   +2 more sources

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.
K. Hatzikiriakou
openaire   +2 more sources

Algebraic elements in formal power series rings

Israel Journal of Mathematics, 1988
Let 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.
exaly   +3 more sources

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|
G. Chang
openaire   +2 more sources

Formal Power Series Over Strongly Hopfian Rings

Communications in Algebra, 2010
A 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
exaly   +2 more sources

Rings of formal power series with homeomorphic prime spectra

Rendiconti del Circolo Matematico di Palermo, 1992
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
D. Dobbs
openaire   +3 more sources

A survey on iterations in rings of formal power series in one indeterminate

Banach Center Publications, 2023
W. Jabłoński
exaly   +2 more sources

Idempotents of 2 × 2 matrix rings over rings of formal power series

Linear and multilinear algebra, 2020
Let be unitary commutative rings which do not have non-trivial idempotents and let be their direct sum. We describe all idempotents in the matrix ring over the ring of formal power series with coefficients in A and in an arbitrary set of variables X.
V. Drensky
semanticscholar   +1 more source

On a differential equation arising in iteration theory in rings of formal power series in one variable

Lecture Notes in Mathematics, 1985
L Reich, Reich L
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A Note on z-Ideals and z°-Ideals of the Formal Power Series Rings and Polynomial Rings in an Infinite Set of Indeterminates

Algebra Colloquium, 2020
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
A. Maatallah, A. Benhissi
semanticscholar   +1 more source