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ON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGS [PDF]
Journal of Algebraic Systems, 2015 Let $alpha$ be an automorphism of a ring $R$. The authors [On skewinverse Laurent-serieswise Armendariz rings, Comm. Algebra 40(1)(2012) 138-156] applied the concept of Armendariz rings to inverseskew Laurent series rings and introduced skew ...
Mohammad Habibi
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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 +2 more
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Zero-divisor graphs of twisted partial skew generalized power series rings [PDF]
Arab Journal of Mathematical Sciences, 2022 Purpose – The aim of this paper is to investigate the relationship between the ring structure of the twisted partial skew generalized power series ring RG,≤;Θ and the corresponding structure of its zero-divisor graph Γ̅RG,≤;Θ. Design/methodology/approach
Mohammed H. Fahmy +2 more
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Directed zero-divisor graph and skew power series rings [PDF]
Transactions on Combinatorics, 2018 Let $R$ be an associative ring with identity and $Z^{\ast}(R)$ be its set of non-zero zero-divisors. Zero-divisor graphs of rings are well represented in the literature of commutative and non-commutative rings. The directed zero-divisor graph of $R$
Ebrahim Hashemi +2 more
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Prime Graphs of Polynomials and Power Series Over Noncommutative Rings [PDF]
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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Positivity in power series rings [PDF]
advg, 2008 Abstract We extend and generalize results of Scheiderer (2006) on the representation of polynomials nonnegative on two-dimensional basic closed semialgebraic sets. Our extension covers some situations where the defining polynomials do not satisfy the transversality condition.
Jaka Cimprič +2 more
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NILRADICALS OF POWER SERIES RINGS AND NIL POWER SERIES RINGS
Journal of the Korean Mathematical Society, 2005 Let \(R\) be a ring, not necessarily with an identity, and let \(X\) be a nonempty set of indeterminates. \(R[\![X]\!]\) and \(R\{X\}\) denote the power series over \(R\) with \(X\) commuting and when \(X\) is noncommuting, respectively. Earlier results on the nilradical of these rings [\textit{E. R. Puczyłowski} and \textit{A. Smoktunowicz}, Isr.
Chan Huh, Yang Lee
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Weak Normalization of Power Series Rings [PDF]
Canadian Mathematical Bulletin, 1995 AbstractIt is proved that if r* is the weak normalization of an integral domain r, then the weak normalization of the power series ring r[[x1,....xn]] is contained in R*[[X1,....Xn]]. Consequently, if R is a weakly normal integral domain, then R[[X1,....Xn]] is also weakly normal.
David E. Dobbs, Moshe Roitman
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Dimension Theory in Iterated Local Skew Power Series Rings [PDF]
Algebras and Representation Theory, 2022 William Woods
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ALMOST right (left) SEMICLEAN RINGS of SKEW GENERALIZED POWER SERIES
Journal of Scientific Research in ScienceWe 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 +2 more
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