On the Structure of Imbedded Submodules in QTAG-Modules and Their Relation to Direct Sums
DOI:
https://doi.org/10.70917/ijcisim-2026-2553Keywords:
-imbedded submodules, direct sums of uniserial modules, h-pure submodules, QTAG-moduleAbstract
In this paper, we investigate the structure of imbedded submodules in QTAG-modules and their relationship to direct sums of uniserial modules. Imbedded submodules, defined as a natural generalization of -pure submodules, have been shown to be considerably more abundant than -pure submodules on direct sums of uniserial modules . We establish several new results concerning the properties of -imbedded submodules, including a criterion for a submodule to be imbedded and the relationship between imbeddedness and h-purity. In particular, we prove that if is an imbedded submodule of a QTAG-module such that is -divisible, then is -pure in . Furthermore, we characterize imbedded-complete modules and examine the conditions under which direct sums of uniserial modules admit imbedded submodules. Our results demonstrate that imbeddedness provides a more flexible framework than -purity for studying the structure of QTAG-modules
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