Lattice of Subinjective Portfolios of Modules

Authors : Yilmaz Durğun

Pages : 11-19

Doi:10.53570/jnt.1467235

View : 88 | Download : 97

Publication Date : 2024-06-30

Article Type : Research Paper

Abstract :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.
Keywords : Subinjectivity domain, subinjective profile, complete lattice of subinjectivity domains