Tsukuba Journal of Mathematics
- Tsukuba J. Math.
- Volume 38, Number 1 (2014), 25-37.
Goldie extending modules and generalizations of quasi-continuous modules
A module M is said to be quasi-continuous if it is extending with the condition (C3) (cf. , ). In this paper, by using the notion of a G-extending module which is defined by E. Akalan, G. F. Birkenmeier and A. Tercan , 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. ). 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.
Tsukuba J. Math., Volume 38, Number 1 (2014), 25-37.
First available in Project Euclid: 13 August 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 16D10: General module theory
Secondary: 16D50: Injective modules, self-injective rings [See also 16L60]
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