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

Natnael Teshale Amare

doi:10.18778/0138-0680.2024.16

Authors

Natnael Teshale Amare University of Gondar, Department of Mathematics https://orcid.org/0000-0001-5771-0757

DOI:

https://doi.org/10.18778/0138-0680.2024.16

Keywords:

weakly 1-absorbing prime ideal, weakly 1−absorbing prime filter, \(\mathcal{L}\)−weakly 2−absorbing ideal, \(\mathcal{L}\)−weakly 1−absorbing prime ideal, \(\mathcal{L}\)−weakly 2−absorbing filter, \(\mathcal{L}\)−weakly 1−absorbing prime filter

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).

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