University of Guilan Journal of Algebra and Related Topics 2345-3931 14 Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024). 2026 04 01 $1$-Absorbing prime property in lattices 1 14 8183 10.22124/jart.2024.28061.1693 EN Sh. Ebrahimi Atani Department of Pure Mathematics, University of Guilan, Rasht, Iran 0009-0001-2215-9640 Journal Article 2024 07 31 Let $\pounds$ be a bounded distributive lattice. Following the concept of $1$-absorbing prime ideal, we define $1$-absorbing prime filters of $\pounds$. A proper filter $F$ of $\pounds$ is called $1$-absorbing prime filter of $\pounds$ if whenever non-zero elements $a, b, c \in \pounds$ and $a \vee b \vee c \in F$, then either $a \vee b \in F$ or $c \in F$. We will make an intensive investigate the basic properties and possible structures of these filters. https://jart.guilan.ac.ir/article_8183_3757f4baa8dda28f3be387e4996cd263.pdf