On preenvelopes and precovers by ideals of morphisms of modules

Let I be a left or right ideal of the category of left R-modules. We first study the closure properties of I-preenvelopes and I-precovers of modules under direct sums, direct products and extensions. Then we explore the relationship between I-preenvelopes (I-precovers) of modules and that of morphisms. As a consequence, we obtain the existence of I-preenvelopes and I-precovers of modules for some special ideals I.