Results 141 to 150 of about 183 (174)

NOETHERIAN GENERALIZED POWER SERIES RINGS AND MODULES

Communications in Algebra, 2001
In this paper we considerably strengthen a result of Ribenboim on noetherian generalised power series rings. While Ribenboim proves his result under the restrictive assumption that the monoid occuring in the definition of the geralised power series ring in cancellative we prove a corresponding result for arbitrary ordered monoids.
K Varadarajan
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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
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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.
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Krull property of generalized power series rings

Journal of Pure and Applied Algebra, 2023
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Park, M. H., Oh, D. Y.
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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 ...
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On the generalized Krull property in power series rings

Journal of Pure and Applied Algebra, 2020
A generalized Krull domain is a domain \(R\) with a family \((R_{\alpha})_{\alpha\in\Lambda}\) of valuation overrings satisfying: (a) \(\displaystyle R=\bigcap_{\alpha\in\Lambda}R_{\alpha}\). (b) The family \((R_{\alpha})_{\alpha\in\Lambda}\) has a finite character. (c) Each \(R_{\alpha}\) is the localization of \(R\) at \(M_{\alpha}\cap R\) where \(M_{
Giau L.T.N., Kang B.G., Toan P.T.
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Ordered Rings of Generalized Power Series

1993
In this paper, we consider orders on rings of generalized power series. Unless the contrary is expressly stated, we do not assume the orders to be total (=linear); for brevity we omit the qualification “partial” order. The first section deals with the order introduced by Conrad, Harvey & Holland on abelian additive groups of maps from an ordered set (S,
A. Benhissi, P. Ribenboim
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An Alternative Perspective on Skew Generalized Power Series Rings

Mediterranean Journal of Mathematics, 2016
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Alhevaz, Abdollah, Hashemi, Ebrahim
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Morita Duality for the Rings of Generalized Power Series

Acta Mathematica Sinica, English Series, 2002
Let \(A,B\) be associative rings with identity, and \((S,\leq)\) be a strictly totally ordered monoid which is also Artinian and finitely generated. Then one forms a ring, denoted by \([[A^{S,\leq}]]\), called the ring of generalized power series. For any bimodule \(_AM_B\), one forms a bimodule \(_{[[A^{S,\leq}]]}[M^{S,\leq}]_{[[B^{S,\leq}]]}\).
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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
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