Results 221 to 230 of about 9,360 (253)

Special Properties of Rings of Generalized Power Series

Communications in Algebra, 2004
Abstract Let R be a ring and (S, ≤) a strictly ordered monoid. Properties of the ring [[R S,≤]] of generalized power series with coefficients in R and exponents in S are considered in this paper. It is shown that [[R S,≤]] is reduced (2-primal, Dedekind finite, clean, uniquely clean) if and only if R is reduced (2-primal, Dedekind finite, clean ...
Zhongkui Liu
exaly   +2 more sources

Nil-Armendariz Condition on Skew Generalized Power Series Rings

Iranian Journal of Science and Technology, Transaction A: Science, 2017
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Raoufeh Manaviyat, Mohammad Habibi
exaly   +3 more sources

Krull Domains of Generalized Power Series

Journal of Algebra, 2001
For an integral domain D and a torsion-free cancellative strictly subtotally ordered monoid (S,≤), it is shown that the generalized power series ring [[DS,≤]] is a Krull domain if and only if D is a Krull domain and S is a Krull ...
Hwankoo Kim
exaly   +2 more sources

The ascending chain condition for principal left or right ideals of skew generalized power series rings

Journal of Algebra, 2009
Let R be a ring, S a monoid and ω:S→End(R) a monoid homomorphism. In this paper we prove that if the monoid S is strictly totally ordered or S is commutative torsion-free cancellative semisubtotally ordered, then the ring R〚S,ω〛 of skew generalized power
Ryszard Mazurek, Michał Ziembowski
exaly   +2 more sources

Generalization of Artinian rings and the formal power series rings

Rendiconti del Circolo Matematico di Palermo Series 2, 2022
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Maaref, Walid, Hamed, Ahmed, Benhissi, Ali   +2 more
openaire   +1 more source

Quasi-Armendariz generalized power series rings

Journal of Algebra and Its Applications, 2016
Let [Formula: see text] be a ring, [Formula: see text] a strictly ordered monoid and [Formula: see text] a monoid homomorphism. The skew generalized power series ring [Formula: see text] is a common generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomial rings, (skew) group rings, and Mal’cev–Neumann Laurent ...
Paykan, K., Moussavi, A.
openaire   +1 more source

Krull property of generalized power series rings

Journal of Pure and Applied Algebra, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Park, M. H., Oh, D. Y.
openaire   +2 more sources

RADICALS OF SKEW GENERALIZED POWER SERIES RINGS

Journal of Algebra and Its Applications, 2012
Let R be a ring, (S, ≤) a strictly ordered monoid and ω : S → End (R) a monoid homomorphism. In this note for a (S, ω)-Armendariz ring R we study some properties of skew generalized power series ring R[[S, ω]]. In particular, among other results, we show that for a S-compatible (S, ω)-Armendariz ring R, α(R[[S, ω]]) = α(R)[[S, ω]] = Ni ℓ*(R)[[S, ω ...
openaire   +1 more source

An Alternative Perspective on Skew Generalized Power Series Rings

Mediterranean Journal of Mathematics, 2016
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Alhevaz, Abdollah, Hashemi, Ebrahim
openaire   +2 more sources

On semilocal, Bézout and distributive generalized power series rings

International Journal of Algebra and Computation, 2015
Let R be a ring, and let S be a strictly ordered monoid. The generalized power series ring R[[S]] is a common generalization of polynomial rings, Laurent polynomial rings, power series rings, Laurent series rings, Mal'cev–Neumann series rings, monoid rings and group rings.
Ryszard Mazurek, Michal Ziembowski
openaire   +2 more sources