Given a ring R, we study its right subinjective profile siP(R) to be the collection of subinjectivity domains of its right R-modules. We deal with the lattice structure of the class siP(R). We show that the poset (siP(R),⊆) forms a complete lattice, and an indigent R-module exists if siP(R) is a set. In particular, if R is a generalized uniserial ring with J²(R)=0, then the lattice (siP(R),⊆,, ) is Boolean.
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Yılmaz Durğun (2024) studied this question.