\(\mathcal{L}\)−weakly 1−Absorbing Prime Ideals and Filters

Abstract

In this manuscript, we have presented the concept of \(\mathcal{L}\)-weakly 1-absorbing prime ideals and \(\mathcal{L}\)-weakly 1-absorbing prime filters within an ADL. Mainly, we illustrate the connections between \(\mathcal{L}\)-weakly prime ideals (filters) and \(\mathcal{L}\)-weakly 1-absorbing prime ideals (filters), as well as between \(\mathcal{L}\)-weakly 1-absorbing prime ideals (filters) and \(\mathcal{L}\)-weakly 2-absorbing ideals (filters). Lastly, we have shown that both the image and inverse image of \(\mathcal{L}\)-weakly 1-absorbing prime ideals (filters) result in \(\mathcal{L}\)-weakly 1-absorbing prime ideals (filters).