On $n$-Absorbing Ideals in a Lattice

Ali Akbar Estaji, Toktam Haghdadi

Let $L$ be a lattice, and let $n$ be a positive integer. In this article, we introduce $n$-absorbing ideals in $L$. We give some properties of such ideals. We show that every $n$-absorbing ideal $I$ of $L$ has at most $n$ minimal prime ideals. Also, we give some properties of $2$-absorbing and weakly $2$-absorbing ideals in $L$. In particular we show that in every non-zero distributive lattice $L$, $2$-absorbing and weakly $2$-absorbing ideals are equivalent.