Results 51 to 60 of about 32,538 (166)
Seminormality in power series rings
Journal of Algebra, 1983 Let R be a commutative unitary ring. Recently, several authors have been interested in the preservation of seminormality in passing from R to the polynomial ring R [X, ,..., X,,J. In this paper we give a proof in the case of power series rings and the proof is both short and applicable in the polynomial setting.
Brewer, J.W, Nichols, Warren D
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On Magnus' Freiheitssatz and free polynomial algebras [PDF]
International Journal of Group Theory, 2015 The Freiheitssatz of Magnus for one-relator groups is one of the cornerstones of combinatorial group theory. In this short note which is mostly expository we discuss the relationship between the Freiheitssatz and corre- sponding results in free power ...
Benjamin Fine +2 more
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Power series rings and projectivity [PDF]
manuscripta mathematica, 2005 Mainly thanks to remarks and pointers by L.L.Avramov and S.Iyengar, we added further context and references. To appear in Manuscripta Mathematica.
Buchweitz, Ragnar-Olaf, Flenner, Hubert
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Prime Graphs of Polynomials and Power Series Over Noncommutative Rings
International Journal of Mathematics and Mathematical SciencesThe prime graph PGR of a ring R is a graph whose vertex set consists of all elements of R. Two elements x,y∈R are adjacent in the graph if and only if xRy=0 or yRx=0.
Walaa Obaidallah Alqarafi +2 more
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Bezout and semihereditary power series rings
Journal of Algebra, 2003 Throughout the paper all rings are associative with 1. For a ring \(R\), \(R[\![x]\!]\) denotes the ring of power series on one commuting variable \(x\) and with coefficients in \(R\). A ring \(R\) is said to be left (right) \(\aleph_0\)-injective provided any homomorphism from a countably generated left (right) ideal of \(R\) into \(R\) extends to a ...
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On z-Ideals and z ◦ -Ideals of Power Series Rings
Journal of Mathematical Extension, 2013 Let R be a commutative ring with identity and R[[x]] be the ring of formal power series with coefficients in R. In this article we consider sufficient conditions in order that P[[x]] is a minimal prime ideal of R[[x]] for every minimal prime ideal P ...
A. Rezaei Aliabad, R. Mohamadian
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Some Connections Between Classical Coding and Network Coding Over Erroneous Cyclic Networks
IEEE Access, 2016 Recently, a framework was given for linear error-correcting network codes (LENCs) over cyclic networks on commutative rings. When the alphabet is considered as a rational power series ring, an LENC is referred to as a convolutional error-correcting ...
Vahid Samadi-Khaftari +2 more
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S-J-Ideals: A Study in Commutative and Noncommutative Rings
Journal of MathematicsIn this paper, we introduce the concept of S-J-ideals in both commutative and noncommutative rings. For a commutative ring R and a multiplicatively closed subset S, we show that many properties of J-ideals apply to S-J-ideals and examine their ...
Alaa Abouhalaka +2 more
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Weak normalisation and the power series rings
Journal of Pure and Applied Algebra, 1996 We follow the notations of \textit{D. E. Dobbs} and \textit{M. Roitman} in Can. Math. Bull. 38, No. 4, 429-433 (1995; Zbl 0848.13019) with the difference that A and B are commutative rings and not necessarily integral domains. The main theorem says that if \(A \subset B\), then the weak normalization of \(A[[X]]\) in \(B[[X]]\) is contained in the ...
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A remark on power series rings [PDF]
Publicacions Matemàtiques, 1992 A trivializability principle for local rings is described which leads to a form of weak algorithm for local semifirs with a finitely generated maximal ideal whose powers meet in zero.
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