\(L\)−weakly 1−Absorbing Prime Ideals and Filters - Amare, Natnael Teshale (Bulletin of the Section of Logic, 2024)
In this manuscript, we have presented the concept of \(L\)-weakly 1-absorbing prime ideals and \(L\)-weakly 1-absorbing prime filters within an ADL. Mainly, we illustrate the connections between \(L\)-weakly prime ideals (filters) and \(L\)-weakly 1-absorbing prime ideals (filters), as well as between \(L\)-weakly 1-absorbing prime ideals (filters) and \(L\)-weakly 2-absorbing ideals (filters). Lastly, we have shown that both the image and inverse image of \(L\)-weakly 1-absorbing prime ideals (filters) result in \(L\)-weakly 1-absorbing prime ideals (filters).