Results 11 to 20 of about 314 (211)

The ascending chain condition for principal left or right ideals of skew generalized power series rings

Journal of Algebra, 2009
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Ryszard Mazurek, Michał Ziembowski
exaly   +4 more sources

On Nilpotent Elements, Weak Symmetry and Related Properties of Skew Generalized Power Series Rings

Symmetry
The skew generalized power series ring R[[S,ω]] is a ring construction involving a ring R, a strictly ordered monoid (S,≤), and a monoid homomorphism ω:S→End(R). The ring R[[S,ω]] is a common generalization of ring extensions such as (skew) polynomial rings, (skew) Laurent polynomial rings, (skew) power series rings, (skew) Laurent series rings, (skew)
Ryszard Mazurek, Mazurek Ryszard
exaly   +3 more sources

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
openaire   +4 more sources

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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IDEMPOTENT MATRIX OVER SKEW GENERALIZED POWER SERIES RINGS

Journal of Fundamental Mathematics and Applications (JFMA), 2022
Let $R[[S,\leq,\omega]]$ be a skew generalized power series ring, with $R$ is a ring with an identity element, $(S,\leq)$ a strictly ordered monoid, and $\omega:S\rightarrow End(R)$ a monoid homomorphism. We define  the set of all matrices over $R[[S,\leq,\omega]]$, denoted by $M_{n}(R[[S,\leq,\omega]])$.
Ahmad Faisol, Fitriani Fitriani
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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
doaj   +3 more sources

On zip and weak zip rings of skew generalized power series

Journal of the Egyptian Mathematical Society, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Salem, R.M.
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ZERO DIVISOR GRAPHS OF SKEW GENERALIZED POWER SERIES RINGS

Communications of the Korean Mathematical Society, 2015
Let R be a ring, (S, ) a strictly ordered monoid and ! : S ! End(R) a monoid homomorphism. The skew generalized power se- ries ring R((S,!)) 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.
A Moussavi, Kamal Paykan
exaly   +3 more sources

PF-rings of skew generalized power series

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 $q \in Q$.
exaly   +3 more sources

Generalized Baer and Generalized Quasi-Baer Rings of Skew Generalized Power Series

Let $R$ be a ring with identity, $(S,\leq)$ an ordered monoid, $ω:S \to End(R)$ a monoid homomorphism, and $A= R\left[\left[S,ω\right]\right]$ the ring of skew generalized power series. The concepts of generalized Baer and generalized quasi-Baer rings are generalization of Baer and quasi-Baer rings, respectively.
Hamam, M. M., Abdel-Khalek, R. E., Salem, R. M.   +2 more
openaire   +3 more sources