This paper is about to find which properties of the (sub-) category of \(R\)-modules reflect the structure of \(R\), where throughout \(R\) is a commutative ring with unit and any module is unital. For a recent work in the same direction see [\textit{R. Takahashi}, ``When is there a nontrivial extension-closed subcategory?'', J. Algebra 331, No. 1, 388--399 (2011; Zbl 1233.13004)]. The authors consider a subcategory (here we denote it by \(\mathcal{D}\)) of the category of \(R\)-modules whose objects are direct sum of all cyclic modules. While classical works such as [\textit{G. Köthe}, ``Verallgemeinerte Abelsche Gruppen mit hyperkomplexem Operatorenring'', Math. Z. 39, 31--44 (1934; Zbl 0010.01102)] study the rings where \(\mathcal{D}\) is equal to the category of \(R\)-modules. The authors ask for \textit{when does \(\mathcal{D}\) contain the category of ideals of \(R\). \((\ast)\)} It is shown that when \(R\) is Noetherian and satisfies \((\ast)\) then the Krull dimension of \(R\) is at most \(1\) and if in addition \(R\) is local then \(\mathrm{Spec}(R)\) has at most 3 elements (Theorem 2.5). In Theorem 2.13, the authors give a characterization for rings which are a finite direct sum of Noetherian local rings and satisfies \((\ast)\). In the last section they present several examples to show that the obtained properties (or even the known ones) are not preserved once one restricts (or extends) \(\mathcal{D}\) (or the category of ideals) and impose the same condition \((\ast)\), for instance it is shown that \((\ast)\) is not a local property.