Remarks Concerning Certain Function Rings in Pointfree Topology

Abstract

For the $\ell$-ring F(L) introduced in Karimi Feizabadi et al. (Categ Gen Algebr Struct Appl 5:85–102, 2016) and then shown to have an embedding into the familiar $\ell$-ring ${\mathfrak R}L$ of all real-valued continuous function on a frame L, the resulting image ${\mathfrak S}L$ in ${\mathfrak R}L$ is characterized here by internal properties within ${\mathfrak R}L$. Further, a number of results concerning the ${\mathfrak S}L$ are obtained on the basis of this characterization.