Results 11 to 20 of about 3,987 (248)

LEFT APP-RINGS OF SKEW GENERALIZED POWER SERIES [PDF]

Journal of Algebra and Its Applications, 2011
A ring R is called a left APP-ring if the left annihilator lR(Ra) is right s-unital as an ideal of R for any a ∈ R. Let R be a ring, (S, ≤) be a commutative strictly ordered monoid and ω: S → End (R) be a monoid homomorphism. The skew generalized power series ring [[RS, ≤, ω]] is a common generalization of (skew) polynomial rings, (skew) power series ...
RENYU ZHAO
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On t-closedness of generalized power series rings

Journal of Pure and Applied Algebra, 2002
Let \(A\subset B\) be an extension of commutative rings. We say that \(A\) is \(t\)-closed in \(B\) if, whenever \(b^2-ab\), \(b^3-ab^2\in A\) for \(a\in A\) and \(b\in B\), then \(b\in A\). We say that property \({\mathcal P}_1(A,B)\) holds if, whenever \(ab\in A\) for \(a\in A\) and \(b\in B\), then \(ab^2\in A\).
Hwankoo Kim, Kim, Hwankoo
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ALMOST right (left) SEMICLEAN RINGS of SKEW GENERALIZED POWER SERIES

Journal of Scientific Research in Science
We extend the notions of almost clean, n-almost clean, and almost semiclean to the non-commutative setting. Then, we demonstrate that under specific conditions that the skew generalized power series rings S[[T,w]] is almost right (left) semiclean if ...
Dina Abdelhakim, Refaat Salem, Sarah El-Din   +2 more
doaj   +2 more sources

PS-Modules over Ore Extensions and Skew Generalized Power Series Rings [PDF]

International Journal of Mathematics and Mathematical Sciences, 2015
A right R-module MR is called a PS-module if its socle, SocMR, is projective. We investigate PS-modules over Ore extension and skew generalized power series extension.
Refaat M. Salem, Mohamed A. Farahat, Hanan Abd-Elmalk   +2 more
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A STUDY OF DERIVATIONS AND LINEAR MAPPINGS ON SKEW GENERALIZED POWER SERIES MODULES

Barekeng
This paper investigates the structure of skew generalized power series modules over skew generalized power series rings, emphasizing the extension of derivations in this context. We define and study additive mappings that generalize classical derivations
Ahmad Faisol, Fitriani Fitriani
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REVERSIBLE SKEW GENERALIZED POWER SERIES RINGS [PDF]

Bulletin of the Australian Mathematical Society, 2011
AbstractIn this note we show that there exist a semiprime ring R, a strictly ordered artinian, narrow, unique product monoid (S,≤) and a monoid homomorphism ω:S⟶End(R) such that the skew generalized power series ring R[[S,ω]] is semicommutative but R[[S,ω]] is not reversible. This answers a question posed in Marks et al. [‘A unified approach to various
A. R. NASR-ISFAHANI, Nasr-Isfahani, Alireza   +1 more
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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
Ribenboim, P.
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On n-root closedness of generalized power series rings over pairs of rings

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, Liu Zhongkui
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Existence of prime elements in rings of generalized power series [PDF]

Journal of Symbolic Logic, 2001
AbstractThe fieldK((G)) of generalized power series with coefficients in the fieldKof characteristic 0 and exponents in the ordered additive abelian groupGplays an important role in the study of real closed fields. Conway and Gonshor (see [2, 4]) considered the problem of existence of non-standard irreducible (respectively prime) elements in the huge ...
Pitteloud, D
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Noetherian rings of generalized power series

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.
Ribenboim, Paulo
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