Results 211 to 220 of about 3,987 (248)

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
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PP-Rings of Generalized Power Series

Acta Mathematica Sinica, English Series, 2000
English translation of the article reviewed above (Zbl 1015.16045).
Liu Zhongkui
exaly   +3 more sources

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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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
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Noetherian Generalized Power Series Rings

Communications in Algebra, 2004
Abstract Let R be a unitary ring and (M, ≤) a strictly ordered monoid. We show that, if (M, ≤) is positively ordered, then the generalized power series ring R[[M, ≤]] is left Noetherian, if and only if, R is left Noetherian and M is finitely generated, if and only if, R is left Noetherian and R[[M, ≤]] is a homomorphic image of the power series ring R[[
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Generalized Power Series Rings

, 1990
Let R be a commutative ring, with unit element 1. Let S be a commutative monoid written multiplicatively (except when written additively...); thus, S is a semigroup with unit element, also denoted 1. We assume that S is endowed with a compatible strict order relation ≤, which is not necessarily a total order.
P. Ribenboim
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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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On app skew generalized power series rings

Studia Scientiarum Mathematicarum Hungarica, 2013
By [12], a ring R is left APP if R has the property that “the left annihilator of a principal ideal is pure as a left ideal”. Equivalently, R is a left APP-ring if R modulo the left annihilator of any principal left ideal is flat. Let R be a ring, (S, ≦) a strictly totally ordered commutative monoid and ω: S → End(R) a monoid homomorphism.
A. Majidinya, A. Moussavi
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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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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
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