Tsukuba Journal of Mathematics

Goldie extending modules and generalizations of quasi-continuous modules

Yosuke Kuratomi

Full-text: Open access

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.

Article information

Source
Tsukuba J. Math., Volume 38, Number 1 (2014), 25-37.

Dates
First available in Project Euclid: 13 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1407938670

Digital Object Identifier
doi:10.21099/tkbjm/1407938670

Mathematical Reviews number (MathSciNet)
MR3261911

Zentralblatt MATH identifier
1318.16006

Subjects
Primary: 16D10: General module theory
Secondary: 16D50: Injective modules, self-injective rings [See also 16L60]

Keywords
Goldie-extending module ejective module finite internal exchange property

Citation

Kuratomi, Yosuke. Goldie extending modules and generalizations of quasi-continuous modules. Tsukuba J. Math. 38 (2014), no. 1, 25--37. doi:10.21099/tkbjm/1407938670. https://projecteuclid.org/euclid.tkbjm/1407938670


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