Results 21 to 30 of about 9,861,726 (254)
Rings of Generalized Power Series
Journal of Algebra, 1994 [For part I see Abh. Math. Semin. Univ. Hamb. 61, 15-33 (1991; Zbl 0751.13005).] Consider a strictly ordered monoid \(S\) and a commutative ring \(R\) with unit element. A generalized power series with coefficients in \(R\) and exponents in \(S\) is a mapping \(f:S \to R\) having artinian and narrow support \((\text{supp} (f))\), that is every strictly
Paulo Ribenboim
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Noetherian rings of generalized power series [PDF]
Journal of Pure and Applied Algebra, 1992 Rings of generalized power series include, as particular cases, monoid rings, ordinary formal power series rings, rings of arithmetical functions, etc. The paper investigates when a ring of generalized power series is noetherian. As a consequence, many interesting classes of examples of noetherian rings are obtained.
Paulo Ribenboim
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S-Noetherian generalized power series rings [PDF]
, 2016 Let R be a ring with identity, (M;\leq) a commutative positive strictly ordered monoid and w_m an automorphism for each m \in M . The skew generalized power series ring R[[M,w]] is a common generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomial rings, (skew) group rings, and Mal'cev Neumann Laurent series rings.
Farzad Padashnik +2 more
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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_{
Le Thi Ngoc Giau +2 more
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Semisimple Rings and Von Neumann Regular Rings of Generalized Power Series [PDF]
Journal of Algebra, 1997 Let \((S,+,\leq)\) be a strictly ordered monoid and let \(R\) be a ring. The author defines the ring of generalized power series \(A=[R^{S,\leq}]\), with coefficients in \(R\) and exponents in \(S\) as the set of all functions \(f\colon S\to R\) such that \(\text{supp}(f)\) is artinian and narrow. The following main theorem is proved. Let \(R\) contain
Paulo Ribenboim
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On zip and weak zip rings of skew generalized power series [PDF]
Journal of the Egyptian Mathematical Society, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
R. Salem
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Unique factorization in generalized power series rings [PDF]
Proceedings of the American Mathematical Society, 2005 Let K K be a field of characteristic zero and let
James Pommersheim, Shahriar Shahriari
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Nilpotent Elements and Nil-Reflexive Property of Generalized Power Series Rings
Advances in Pure Mathematics, 2022 Eltiyeb Ali
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On n-root closedness of generalized power series rings over pairs of rings [PDF]
Journal of Pure and Applied Algebra, 1999 This paper deals with \(n\)-root closedness of generalized power series rings (as defined by P. Ribenboim), thus generalizing previous results on classical power series rings by \textit{D. F. Anderson, D. E. Dobbs} and \textit{M. Roitman} [J. Pure Appl. Algebra 114, No. 2, 111-131 (1997; Zbl 0926.13012)].
Zhongkui Liu
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Generalized rational identities of power series rings
Journal of Algebra, 1986 Let A be a fixed algebra over a field F and let \(X=\{X_ 1,...,X_ m\}\) be noncommuting variables. Denote by R(X,A) the algebra of all formal rational expressions formed from \(X\cup A\). The ring P is an A-ring if A is a subring of P and the centre of P contains that of A. One says that \(f(X_ 1,...,X_ m)\in R(X,A)\) is a generalized rational identity
Jerry D. Rosen, Mary Peles Rosen
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