Lattice of Subinjective Portfolios of Modules
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
Supporting Institution
The Scientific and Technological Research Council of T\"{u}rkiye (TUBITAK)
Project Number
122F130
Ethical Statement
The author declares no conflict of interest.
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