Lattice of Subinjective Portfolios of Modules

Year 2024, Issue: 47, 11 - 19, 30.06.2024

Yilmaz Durğun

https://doi.org/10.53570/jnt.1467235

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

Ethical Statement

The author declares no conflict of interest.

Supporting Institution

The Scientific and Technological Research Council of T\"{u}rkiye (TUBITAK)

Project Number

122F130

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