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July 2014 Goldie extending modules and generalizations of quasi-continuous modules
Yosuke Kuratomi
Tsukuba J. Math. 38(1): 25-37 (July 2014). DOI: 10.21099/tkbjm/1407938670

Abstract

A module M is said to be quasi-continuous if it is extending with the condition (C3) (cf. [7], [10]). In this paper, by using the notion of a G-extending module which is defined by E. Akalan, G. F. Birkenmeier and A. Tercan [1], we introduce a generalization of quasi-continuous “a GQC (generalized quasicontinuous)-module” and investigate some properties of GQC-modules. Initially we give some properties of a relative ejectivity which is useful in analyzing the structure of G-extending modules and GQC-modules (cf. [1]). And we apply them to the study of direct sums of GQC-modules. We also prove that any direct summand of a GQC-module with the finite internal exchange property is GQC. Moreover, we show that a module M is G-extending modules with (C3) if and only if it is GQC-module with the finite internal exchange property.

Citation

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Yosuke Kuratomi. "Goldie extending modules and generalizations of quasi-continuous modules." Tsukuba J. Math. 38 (1) 25 - 37, July 2014. https://doi.org/10.21099/tkbjm/1407938670

Information

Published: July 2014
First available in Project Euclid: 13 August 2014

zbMATH: 1318.16006
MathSciNet: MR3261911
Digital Object Identifier: 10.21099/tkbjm/1407938670

Subjects:
Primary: 16D10
Secondary: 16D50

Rights: Copyright © 2014 University of Tsukuba, Institute of Mathematics

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Vol.38 • No. 1 • July 2014
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