Left APP-property of formal power series rings

Zhongkui Liu; Xiao Yan Yang

Displaying similar documents to “Left APP-property of formal power series rings”

On a theorem of McCoy

Rajendra K. Sharma, Amit B. Singh (2024)

Mathematica Bohemica

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We study McCoy’s theorem to the skew Hurwitz series ring $(HR, ω)$ for some different classes of rings such as: semiprime rings, APP rings and skew Hurwitz serieswise quasi-Armendariz rings. Moreover, we establish an equivalence relationship between a right zip ring and its skew Hurwitz series ring in case when a ring $R$ satisfies McCoy’s theorem of skew Hurwitz series.

Rings with divisibility on descending chains of ideals

Oussama Aymane Es Safi, Najib Mahdou, Ünsal Tekir (2024)

Czechoslovak Mathematical Journal

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This paper deals with the rings which satisfy $D C C_{d}$ condition. This notion has been introduced recently by R. Dastanpour and A. Ghorbani (2017) as a generalization of Artnian rings. It is of interest to investigate more deeply this class of rings. This study focuses on commutative case. In this vein, we present this work in which we examine the transfer of these rings to the trivial, amalgamation and polynomial ring extensions. We also investigate the relationship between this class of rings...

A commutativity theorem for associative rings

Mohammad Ashraf (1995)

Archivum Mathematicum

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Let $m > 1, s \geq 1$ be fixed positive integers, and let $R$ be a ring with unity $1$ in which for every $x$ in $R$ there exist integers $p = p (x) \geq 0, q = q (x) \geq 0, n = n (x) \geq 0, r = r (x) \geq 0$ such that either $x^{p} [x^{n}, y] x^{q} = x^{r} [x, y^{m}] y^{s}$ or $x^{p} [x^{n}, y] x^{q} = y^{s} [x, y^{m}] x^{r}$ for all $y \in R$ . In the present paper it is shown that $R$ is commutative if it satisfies the property $Q (m)$ (i.e. for all $x, y \in R, m [x, y] = 0$ implies $[x, y] = 0$ ).

Ring extensions with some finiteness conditions on the set of intermediate rings

Ali Jaballah (2010)

Czechoslovak Mathematical Journal

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A ring extension $R \subseteq S$ is said to be FO if it has only finitely many intermediate rings. $R \subseteq S$ is said to be FC if each chain of distinct intermediate rings in this extension is finite. We establish several necessary and sufficient conditions for the ring extension $R \subseteq S$ to be FO or FC together with several other finiteness conditions on the set of intermediate rings. As a corollary we show that each integrally closed ring extension with finite length chains of intermediate rings is necessarily...