Research Information System
Journal of New Theory, no.47, pp.11-19, 2024 (Peer-Reviewed Journal)
Given a ring $R$, we study its right subinjective profile $mathfrak{siP}(R)$ to be the collection of subinjectivity domains of its right $R$-modules. We deal with the lattice structure of the class $mathfrak{siP}(R)$. We show that the poset $(mathfrak{siP}(R),subseteq)$ forms a complete lattice, and an indigent $R$-module exists if $mathfrak{siP}(R)$ is a set. In particular, if $R$ is a generalized uniserial ring with $J^{2}(R)=0$, then the lattice $(mathfrak{siP}(R),subseteq,wedge, vee)$ is Boolean.