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A simple ring over which proper cyclics are continuous is a $\PCI$-ring

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Published:1998-09-01
Printed: Sep 1998

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Abstract

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 Simple rings, $\PCI$-rings, $\PCQI$-rings, continuous modules, quasi-continuous modules

MSC Classifications:

16D50, 16D70 show english descriptions Injective modules, self-injective rings [See also 16L60]
Structure and classification (except as in 16Gxx), direct sum decomposition, cancellation 16D50 - Injective modules, self-injective rings [See also 16L60]
16D70 - Structure and classification (except as in 16Gxx), direct sum decomposition, cancellation