On McCoy condition and semicommutative rings

Mohamed Louzari

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An intermediate ring between a polynomial ring and a power series ring

M. Tamer Koşan, Tsiu-Kwen Lee, Yiqiang Zhou (2013)

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Let R[x] and R[[x]] respectively denote the ring of polynomials and the ring of power series in one indeterminate x over a ring R. For an ideal I of R, denote by [R;I][x] the following subring of R[[x]]: [R;I][x]: = $\sum_{i \geq 0} r_{i} x^{i} \in R [[x]]$ : ∃ 0 ≤ n∈ ℤ such that $r_{i} \in I$ , ∀ i ≥ n. The polynomial and power series rings over R are extreme cases where I = 0 or R, but there are ideals I such that neither R[x] nor R[[x]] is isomorphic to [R;I][x]. The results characterizing polynomial rings or power series rings with...

Extensions of $G M$ -rings

Huanyin Chen, Miaosen Chen (2005)

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It is shown that a ring $R$ is a $G M$ -ring if and only if there exists a complete orthogonal set ${e_{1}, \dots, e_{n}}$ of idempotents such that all $e_{i} R e_{i}$ are $G M$ -rings. We also investigate $G M$ -rings for Morita contexts, module extensions and power series rings.