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Search: All articles in the CMB digital archive with keyword Simple rings

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1. CMB 2014 (vol 57 pp. 511)

Gonçalves, Daniel
Simplicity of Partial Skew Group Rings of Abelian Groups
Let $A$ be a ring with local units, $E$ a set of local units for $A$, $G$ an abelian group and $\alpha$ a partial action of $G$ by ideals of $A$ that contain local units. We show that $A\star_{\alpha} G$ is simple if and only if $A$ is $G$-simple and the center of the corner $e\delta_0 (A\star_{\alpha} G) e \delta_0$ is a field for all $e\in E$. We apply the result to characterize simplicity of partial skew group rings in two cases, namely for partial skew group rings arising from partial actions by clopen subsets of a compact set and partial actions on the set level.

Keywords:partial skew group rings, simple rings, partial actions, abelian groups
Categories:16S35, 37B05

2. CMB 1998 (vol 41 pp. 261)

Barthwal, S.; Jhingan, S.; Kanwar, P.
A simple ring over which proper cyclics are continuous is a $\PCI$-ring
It is shown that simple rings over which proper cyclic right modules are continuous coincide with simple right $\PCI$-rings, introduced by Faith.

Keywords:Simple rings, $\PCI$-rings, $\PCQI$-rings, continuous modules,, quasi-continuous modules
Categories:16D50, 16D70

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