In this paper,potent index of an element and pseudo clean rings are considered.Some properties and examples of pseudo clean rings are given.We also show that Zm is pseudo clean for every 2≤m∈Z and pseudo clean rings are clean.Furthermore,we prove pseudo clean rings are directly finite and have stable range one.
Toxic effects in terms of mitochondria and hereditary substances have been characterized in vitro for individual rare earth elements,while,the joint effects of mixed elements exposure in the population remain ambiguous.Based on the Occupational Chromate Exposure Dynamic Cohort of China,this study investigated the relationship between 15 blood rare earth elements(cerium,dysprosium,erbium,europium,gadolinium,holmium,lanthanum,lutetium,neodymium,praseodymium,samarium,terbium,thulium,yttrium,and ytterbium)and mitochondrial DNA copy number(MtDNACN)as well as peripheral blood lymphocyte micronucleus frequency(MNF).The elastic net was used to select elements highly correlated with effect indicators,whose dose-response relationships were further illustrated by restricted cubic splines.Bayesian kernel regressionwas employed to explore the combined effects of elements and the contributions of single element.The results showed that most rare earth elementswere positively correlatedwith effect indicators,with yttrium showing the strongest association(β(95%CI):0.139(0.1089–0.189)for MtDNACN,0.937(0.345–1.684)for MNF).In the mixed exposure model,with the exposure level fixed at the 50th percentile as the reference,the effect estimates on MtDNACN and MNF increased by 0.228 and 0.598 units,respectively,at the 75th percentile.The single effect analysis implied that yttrium,lanthanum and terbium contributed the most to the elevation of MtDNACN,while yttrium posed the highest risk for genetic damage,accordingly,we provided recommendations to prioritize these elements of concern.In addition,we observed a chief mediating effect of MtDNACN on the elevation of MNF caused by lanthanum,whereas further mechanistic exploration is required to confirm this finding.
