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Uniserial rings of skew generalized power series [PDF]

Journal of Algebra, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
R Mazurek
exaly   +6 more sources

On Bezout and distributive generalized power series rings [PDF]

Journal of Algebra, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
R Mazurek
exaly   +5 more sources

Noetherian properties in composite generalized power series rings [PDF]

Open Mathematics, 2020
Let (Γ,≤)({\mathrm{\Gamma}},\le ) be a strictly ordered monoid, and let Γ⁎=Γ\{0}{{\mathrm{\Gamma}}}^{\ast }\left={\mathrm{\Gamma}}\backslash \{0\}. Let D⊆ED\subseteq E be an extension of commutative rings with identity, and let I be a nonzero proper ...
Lim Jung Wook, Oh Dong Yeol
doaj   +3 more sources

Left-App rings of skew generalized power series [PDF]

Journal of Algebra and Its Applications, 2010
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
core   +6 more sources

On t-closedness of generalized power series rings [PDF]

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 Kım
core   +3 more sources

Noetherian rings of composite generalized power series

Open Mathematics
Let A⊆BA\subseteq B be an extension of commutative rings with identity, (S,≤)\left(S,\le ) a nonzero strictly ordered monoid, and S*=S\{0}{S}^{* }\left=S\backslash \left\{0\right\}.
Oh Dong Yeol
doaj   +3 more sources

PF-rings of skew generalized power series [PDF]

Tbilisi Mathematical Journal, 2011
Let $R$ be a ring which is $S$-compatible and $(S,\omega)$-Armendariz. In this paper, we investigate that the skew generalized power series ring $R[[S,\omega]]$ is a PF-ring if and only if for any two $S$-indexed subsets $P$ and $Q$ of $R$ such that $Q \subseteq ann_R (P)$ and there exists $a\in ann_R (P)$ such that $q a=q$ for all $q \in Q$.
Amit B. Singh
exaly   +4 more sources

Endo-Noetherian Skew Generalized Power Series Rings [PDF]

Assiut University Journal of Multidisciplinary Scientific Research, 2023
Endo-Noetherian modules were introduced by A. Kaidi and E. Sanchez] as a generalization of Noetherian modules. A left Ɍ-module M which satisfies the ascending chain condition for endomorphic kernels is said to be endo-Noetherian.
Ramy Abdel-Khaleq, Refaat Salem, Neamat Mohamed   +2 more
doaj   +2 more sources

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, Ahmed Ageeb Elokl, Ramy Abdel-Khalek   +2 more
doaj   +3 more sources

The Ring Homomorphisms of Matrix Rings over Skew Generalized Power Series Rings [PDF]

Cauchy: Jurnal Matematika Murni dan Aplikasi, 2021
Let  M_n (R_1 [[S_1,≤_1,ω_1]]) and M_n (R_2 [[S_2,≤_2,ω_2]]) be a matrix rings over skew generalized power series rings, where R_1,R_2 are commutative rings with an identity element, (S_1,≤_1 ),(S_2,≤_2 ) are strictly ordered monoids, ω_1:S_1→End(R_1 ),〖
Ahmad Faisol, Fitriani Fitriani
doaj   +2 more sources